From 484d447296a9399ddd3395ad8e6c26193b608728 Mon Sep 17 00:00:00 2001
From: Yacov Manevich <yacov.manevich@avalabs.org>
Date: Tue, 17 Sep 2024 22:11:42 +0200
Subject: [PATCH] Make snowman use snowflake directly instead of snowball

Snowball was introduced in order to improve the stability of snowflake,
by taking into account the history when returning the preference.

However, if deployed with a configuration where the preference is small enough, and a network partition
causes a 50-50 split of the stake, it can actually backfire, as described in 6e1a905.

Additionally, latest research [1] points out that snowflake suffices for snowman.

This commit removes snowball from snowman and adds a test that simulates a mixed network
which runs snowman with and without snowball, and ensures that a mixed network still converges.

[1] https://arxiv.org/abs/2404.14250

Signed-off-by: Yacov Manevich <yacov.manevich@avalabs.org>
---
 chains/manager.go                             |   5 +-
 .../snowball/binary_snowball_test.go          | 139 +++---
 .../snowball/consensus_performance_test.go    |   8 +-
 .../snowball/consensus_reversibility_test.go  |   2 +-
 snow/consensus/snowball/flat_test.go          |   6 +-
 .../consensus/snowball/nnary_snowball_test.go | 133 ------
 snow/consensus/snowball/tree.go               |   2 +-
 snow/consensus/snowball/tree_test.go          | 445 ++++++++++--------
 .../consensus/snowball/unary_snowball_test.go |  76 ---
 snow/consensus/snowman/consensus_test.go      |   6 +-
 snow/consensus/snowman/mixed_test.go          |  55 +++
 snow/consensus/snowman/network_test.go        |   4 +
 snow/consensus/snowman/snowman_block.go       |   2 +-
 snow/consensus/snowman/topological.go         |  10 +-
 snow/consensus/snowman/topological_test.go    |   8 +-
 snow/engine/snowman/config_test.go            |   2 +-
 snow/engine/snowman/engine_test.go            |   4 +-
 vms/platformvm/vm_test.go                     |   2 +-
 18 files changed, 408 insertions(+), 501 deletions(-)
 delete mode 100644 snow/consensus/snowball/nnary_snowball_test.go
 delete mode 100644 snow/consensus/snowball/unary_snowball_test.go
 create mode 100644 snow/consensus/snowman/mixed_test.go

diff --git a/chains/manager.go b/chains/manager.go
index 2fdd3c0b73f9..28f1528bc28e 100644
--- a/chains/manager.go
+++ b/chains/manager.go
@@ -28,6 +28,7 @@ import (
 	"github.com/ava-labs/avalanchego/network"
 	"github.com/ava-labs/avalanchego/network/p2p"
 	"github.com/ava-labs/avalanchego/snow"
+	"github.com/ava-labs/avalanchego/snow/consensus/snowball"
 	"github.com/ava-labs/avalanchego/snow/engine/avalanche/bootstrap/queue"
 	"github.com/ava-labs/avalanchego/snow/engine/avalanche/state"
 	"github.com/ava-labs/avalanchego/snow/engine/avalanche/vertex"
@@ -922,7 +923,7 @@ func (m *manager) createAvalancheChain(
 		return nil, fmt.Errorf("couldn't initialize snow base message handler: %w", err)
 	}
 
-	var snowmanConsensus smcon.Consensus = &smcon.Topological{}
+	var snowmanConsensus smcon.Consensus = &smcon.Topological{Factory: snowball.SnowflakeFactory}
 	if m.TracingEnabled {
 		snowmanConsensus = smcon.Trace(snowmanConsensus, m.Tracer)
 	}
@@ -1321,7 +1322,7 @@ func (m *manager) createSnowmanChain(
 		return nil, fmt.Errorf("couldn't initialize snow base message handler: %w", err)
 	}
 
-	var consensus smcon.Consensus = &smcon.Topological{}
+	var consensus smcon.Consensus = &smcon.Topological{Factory: snowball.SnowflakeFactory}
 	if m.TracingEnabled {
 		consensus = smcon.Trace(consensus, m.Tracer)
 	}
diff --git a/snow/consensus/snowball/binary_snowball_test.go b/snow/consensus/snowball/binary_snowball_test.go
index 968743ef36a8..bd0d7fcf8cd4 100644
--- a/snow/consensus/snowball/binary_snowball_test.go
+++ b/snow/consensus/snowball/binary_snowball_test.go
@@ -19,25 +19,26 @@ func TestBinarySnowball(t *testing.T) {
 	beta := 2
 	terminationConditions := newSingleTerminationCondition(alphaConfidence, beta)
 
-	sb := newBinarySnowball(alphaPreference, terminationConditions, red)
-	require.Equal(red, sb.Preference())
-	require.False(sb.Finalized())
+	sf := newBinarySnowflake(alphaPreference, terminationConditions, red)
 
-	sb.RecordPoll(alphaConfidence, blue)
-	require.Equal(blue, sb.Preference())
-	require.False(sb.Finalized())
+	require.Equal(red, sf.Preference())
+	require.False(sf.Finalized())
 
-	sb.RecordPoll(alphaConfidence, red)
-	require.Equal(blue, sb.Preference())
-	require.False(sb.Finalized())
+	sf.RecordPoll(alphaConfidence, blue)
+	require.Equal(blue, sf.Preference())
+	require.False(sf.Finalized())
 
-	sb.RecordPoll(alphaConfidence, blue)
-	require.Equal(blue, sb.Preference())
-	require.False(sb.Finalized())
+	sf.RecordPoll(alphaConfidence, red)
+	require.Equal(red, sf.Preference())
+	require.False(sf.Finalized())
 
-	sb.RecordPoll(alphaConfidence, blue)
-	require.Equal(blue, sb.Preference())
-	require.True(sb.Finalized())
+	sf.RecordPoll(alphaConfidence, blue)
+	require.Equal(blue, sf.Preference())
+	require.False(sf.Finalized())
+
+	sf.RecordPoll(alphaConfidence, blue)
+	require.Equal(blue, sf.Preference())
+	require.True(sf.Finalized())
 }
 
 func TestBinarySnowballRecordPollPreference(t *testing.T) {
@@ -50,32 +51,32 @@ func TestBinarySnowballRecordPollPreference(t *testing.T) {
 	beta := 2
 	terminationConditions := newSingleTerminationCondition(alphaConfidence, beta)
 
-	sb := newBinarySnowball(alphaPreference, terminationConditions, red)
-	require.Equal(red, sb.Preference())
-	require.False(sb.Finalized())
+	sf := newBinarySnowflake(alphaPreference, terminationConditions, red)
+	require.Equal(red, sf.Preference())
+	require.False(sf.Finalized())
 
-	sb.RecordPoll(alphaConfidence, blue)
-	require.Equal(blue, sb.Preference())
-	require.False(sb.Finalized())
+	sf.RecordPoll(alphaConfidence, blue)
+	require.Equal(blue, sf.Preference())
+	require.False(sf.Finalized())
 
-	sb.RecordPoll(alphaConfidence, red)
-	require.Equal(blue, sb.Preference())
-	require.False(sb.Finalized())
+	sf.RecordPoll(alphaConfidence, red)
+	require.Equal(red, sf.Preference())
+	require.False(sf.Finalized())
 
-	sb.RecordPoll(alphaPreference, red)
-	require.Equal(red, sb.Preference())
-	require.False(sb.Finalized())
+	sf.RecordPoll(alphaPreference, red)
+	require.Equal(red, sf.Preference())
+	require.False(sf.Finalized())
 
-	sb.RecordPoll(alphaConfidence, red)
-	require.Equal(red, sb.Preference())
-	require.False(sb.Finalized())
+	sf.RecordPoll(alphaConfidence, red)
+	require.Equal(red, sf.Preference())
+	require.False(sf.Finalized())
 
-	sb.RecordPoll(alphaConfidence, red)
-	require.Equal(red, sb.Preference())
-	require.True(sb.Finalized())
+	sf.RecordPoll(alphaConfidence, red)
+	require.Equal(red, sf.Preference())
+	require.True(sf.Finalized())
 
-	expected := "SB(Preference = 0, PreferenceStrength[0] = 4, PreferenceStrength[1] = 1, SF(Confidence = [2], Finalized = true, SL(Preference = 0)))"
-	require.Equal(expected, sb.String())
+	expected := "SF(Confidence = [2], Finalized = true, SL(Preference = 0))"
+	require.Equal(expected, sf.String())
 }
 
 func TestBinarySnowballRecordUnsuccessfulPoll(t *testing.T) {
@@ -88,26 +89,26 @@ func TestBinarySnowballRecordUnsuccessfulPoll(t *testing.T) {
 	beta := 2
 	terminationConditions := newSingleTerminationCondition(alphaConfidence, beta)
 
-	sb := newBinarySnowball(alphaPreference, terminationConditions, red)
-	require.Equal(red, sb.Preference())
-	require.False(sb.Finalized())
+	sf := newBinarySnowflake(alphaPreference, terminationConditions, red)
+	require.Equal(red, sf.Preference())
+	require.False(sf.Finalized())
 
-	sb.RecordPoll(alphaConfidence, blue)
-	require.Equal(blue, sb.Preference())
-	require.False(sb.Finalized())
+	sf.RecordPoll(alphaConfidence, blue)
+	require.Equal(blue, sf.Preference())
+	require.False(sf.Finalized())
 
-	sb.RecordUnsuccessfulPoll()
+	sf.RecordUnsuccessfulPoll()
 
-	sb.RecordPoll(alphaConfidence, blue)
-	require.Equal(blue, sb.Preference())
-	require.False(sb.Finalized())
+	sf.RecordPoll(alphaConfidence, blue)
+	require.Equal(blue, sf.Preference())
+	require.False(sf.Finalized())
 
-	sb.RecordPoll(alphaConfidence, blue)
-	require.Equal(blue, sb.Preference())
-	require.True(sb.Finalized())
+	sf.RecordPoll(alphaConfidence, blue)
+	require.Equal(blue, sf.Preference())
+	require.True(sf.Finalized())
 
-	expected := "SB(Preference = 1, PreferenceStrength[0] = 0, PreferenceStrength[1] = 3, SF(Confidence = [2], Finalized = true, SL(Preference = 1)))"
-	require.Equal(expected, sb.String())
+	expected := "SF(Confidence = [2], Finalized = true, SL(Preference = 1))"
+	require.Equal(expected, sf.String())
 }
 
 func TestBinarySnowballAcceptWeirdColor(t *testing.T) {
@@ -120,36 +121,36 @@ func TestBinarySnowballAcceptWeirdColor(t *testing.T) {
 	beta := 2
 	terminationConditions := newSingleTerminationCondition(alphaConfidence, beta)
 
-	sb := newBinarySnowball(alphaPreference, terminationConditions, red)
+	sf := newBinarySnowflake(alphaPreference, terminationConditions, red)
 
-	require.Equal(red, sb.Preference())
-	require.False(sb.Finalized())
+	require.Equal(red, sf.Preference())
+	require.False(sf.Finalized())
 
-	sb.RecordPoll(alphaConfidence, red)
-	sb.RecordUnsuccessfulPoll()
+	sf.RecordPoll(alphaConfidence, red)
+	sf.RecordUnsuccessfulPoll()
 
-	require.Equal(red, sb.Preference())
-	require.False(sb.Finalized())
+	require.Equal(red, sf.Preference())
+	require.False(sf.Finalized())
 
-	sb.RecordPoll(alphaConfidence, red)
+	sf.RecordPoll(alphaConfidence, red)
 
-	sb.RecordUnsuccessfulPoll()
+	sf.RecordUnsuccessfulPoll()
 
-	require.Equal(red, sb.Preference())
-	require.False(sb.Finalized())
+	require.Equal(red, sf.Preference())
+	require.False(sf.Finalized())
 
-	sb.RecordPoll(alphaConfidence, blue)
+	sf.RecordPoll(alphaConfidence, blue)
 
-	require.Equal(red, sb.Preference())
-	require.False(sb.Finalized())
+	require.Equal(blue, sf.Preference())
+	require.False(sf.Finalized())
 
-	sb.RecordPoll(alphaConfidence, blue)
+	sf.RecordPoll(alphaConfidence, blue)
 
-	require.Equal(blue, sb.Preference())
-	require.True(sb.Finalized())
+	require.Equal(blue, sf.Preference())
+	require.True(sf.Finalized())
 
-	expected := "SB(Preference = 1, PreferenceStrength[0] = 2, PreferenceStrength[1] = 2, SF(Confidence = [2], Finalized = true, SL(Preference = 0)))"
-	require.Equal(expected, sb.String())
+	expected := "SF(Confidence = [2], Finalized = true, SL(Preference = 0))"
+	require.Equal(expected, sf.String())
 }
 
 func TestBinarySnowballLockColor(t *testing.T) {
diff --git a/snow/consensus/snowball/consensus_performance_test.go b/snow/consensus/snowball/consensus_performance_test.go
index dbd3d95e6730..cb66637a3c63 100644
--- a/snow/consensus/snowball/consensus_performance_test.go
+++ b/snow/consensus/snowball/consensus_performance_test.go
@@ -28,10 +28,10 @@ func TestDualAlphaOptimization(t *testing.T) {
 		source        = prng.NewMT19937()
 	)
 
-	singleAlphaNetwork := NewNetwork(SnowballFactory, params, numColors, source)
+	singleAlphaNetwork := NewNetwork(SnowflakeFactory, params, numColors, source)
 
 	params.AlphaPreference = params.K/2 + 1
-	dualAlphaNetwork := NewNetwork(SnowballFactory, params, numColors, source)
+	dualAlphaNetwork := NewNetwork(SnowflakeFactory, params, numColors, source)
 
 	source.Seed(seed)
 	for i := 0; i < numNodes; i++ {
@@ -61,8 +61,8 @@ func TestTreeConvergenceOptimization(t *testing.T) {
 		source           = prng.NewMT19937()
 	)
 
-	treeNetwork := NewNetwork(SnowballFactory, params, numColors, source)
-	flatNetwork := NewNetwork(SnowballFactory, params, numColors, source)
+	treeNetwork := NewNetwork(SnowflakeFactory, params, numColors, source)
+	flatNetwork := NewNetwork(SnowflakeFactory, params, numColors, source)
 
 	source.Seed(seed)
 	for i := 0; i < numNodes; i++ {
diff --git a/snow/consensus/snowball/consensus_reversibility_test.go b/snow/consensus/snowball/consensus_reversibility_test.go
index 578fea1dea18..da64a3ed4568 100644
--- a/snow/consensus/snowball/consensus_reversibility_test.go
+++ b/snow/consensus/snowball/consensus_reversibility_test.go
@@ -23,7 +23,7 @@ func TestSnowballGovernance(t *testing.T) {
 		source              = prng.NewMT19937()
 	)
 
-	nBitwise := NewNetwork(SnowballFactory, params, numColors, source)
+	nBitwise := NewNetwork(SnowflakeFactory, params, numColors, source)
 
 	source.Seed(seed)
 	for i := 0; i < numRed; i++ {
diff --git a/snow/consensus/snowball/flat_test.go b/snow/consensus/snowball/flat_test.go
index 51b7390bb88d..1e9f92b656b0 100644
--- a/snow/consensus/snowball/flat_test.go
+++ b/snow/consensus/snowball/flat_test.go
@@ -20,7 +20,7 @@ func TestFlat(t *testing.T) {
 		AlphaConfidence: 3,
 		Beta:            2,
 	}
-	f := NewFlat(SnowballFactory, params, Red)
+	f := NewFlat(SnowflakeFactory, params, Red)
 	f.Add(Green)
 	f.Add(Blue)
 
@@ -34,7 +34,7 @@ func TestFlat(t *testing.T) {
 
 	twoGreen := bag.Of(Green, Green)
 	require.True(f.RecordPoll(twoGreen))
-	require.Equal(Blue, f.Preference())
+	require.Equal(Green, f.Preference())
 	require.False(f.Finalized())
 
 	threeGreen := bag.Of(Green, Green, Green)
@@ -56,6 +56,6 @@ func TestFlat(t *testing.T) {
 	require.Equal(Green, f.Preference())
 	require.True(f.Finalized())
 
-	expected := "SB(Preference = 2mcwQKiD8VEspmMJpL1dc7okQQ5dDVAWeCBZ7FWBFAbxpv3t7w, PreferenceStrength = 4, SF(Confidence = [2], Finalized = true, SL(Preference = 2mcwQKiD8VEspmMJpL1dc7okQQ5dDVAWeCBZ7FWBFAbxpv3t7w)))"
+	expected := "SF(Confidence = [2], Finalized = true, SL(Preference = 2mcwQKiD8VEspmMJpL1dc7okQQ5dDVAWeCBZ7FWBFAbxpv3t7w))"
 	require.Equal(expected, f.String())
 }
diff --git a/snow/consensus/snowball/nnary_snowball_test.go b/snow/consensus/snowball/nnary_snowball_test.go
deleted file mode 100644
index 8a5e66143db2..000000000000
--- a/snow/consensus/snowball/nnary_snowball_test.go
+++ /dev/null
@@ -1,133 +0,0 @@
-// Copyright (C) 2019-2024, Ava Labs, Inc. All rights reserved.
-// See the file LICENSE for licensing terms.
-
-package snowball
-
-import (
-	"testing"
-
-	"github.com/stretchr/testify/require"
-)
-
-func TestNnarySnowball(t *testing.T) {
-	require := require.New(t)
-
-	alphaPreference, alphaConfidence := 1, 2
-	beta := 2
-	terminationConditions := newSingleTerminationCondition(alphaConfidence, beta)
-
-	sb := newNnarySnowball(alphaPreference, terminationConditions, Red)
-	sb.Add(Blue)
-	sb.Add(Green)
-
-	require.Equal(Red, sb.Preference())
-	require.False(sb.Finalized())
-
-	sb.RecordPoll(alphaConfidence, Blue)
-	require.Equal(Blue, sb.Preference())
-	require.False(sb.Finalized())
-
-	sb.RecordPoll(alphaConfidence, Red)
-	require.Equal(Blue, sb.Preference())
-	require.False(sb.Finalized())
-
-	sb.RecordPoll(alphaPreference, Red)
-	require.Equal(Red, sb.Preference())
-	require.False(sb.Finalized())
-
-	sb.RecordPoll(alphaConfidence, Red)
-	require.Equal(Red, sb.Preference())
-	require.False(sb.Finalized())
-
-	sb.RecordPoll(alphaPreference, Blue)
-	require.Equal(Red, sb.Preference())
-	require.False(sb.Finalized())
-
-	sb.RecordPoll(alphaConfidence, Blue)
-	require.Equal(Red, sb.Preference())
-	require.False(sb.Finalized())
-
-	sb.RecordPoll(alphaConfidence, Blue)
-	require.Equal(Blue, sb.Preference())
-	require.True(sb.Finalized())
-}
-
-func TestVirtuousNnarySnowball(t *testing.T) {
-	require := require.New(t)
-
-	alphaPreference, alphaConfidence := 1, 2
-	beta := 1
-	terminationConditions := newSingleTerminationCondition(alphaConfidence, beta)
-
-	sb := newNnarySnowball(alphaPreference, terminationConditions, Red)
-
-	require.Equal(Red, sb.Preference())
-	require.False(sb.Finalized())
-
-	sb.RecordPoll(alphaConfidence, Red)
-	require.Equal(Red, sb.Preference())
-	require.True(sb.Finalized())
-}
-
-func TestNarySnowballRecordUnsuccessfulPoll(t *testing.T) {
-	require := require.New(t)
-
-	alphaPreference, alphaConfidence := 1, 2
-	beta := 2
-	terminationConditions := newSingleTerminationCondition(alphaConfidence, beta)
-
-	sb := newNnarySnowball(alphaPreference, terminationConditions, Red)
-	sb.Add(Blue)
-
-	require.Equal(Red, sb.Preference())
-	require.False(sb.Finalized())
-
-	sb.RecordPoll(alphaConfidence, Blue)
-	require.Equal(Blue, sb.Preference())
-	require.False(sb.Finalized())
-
-	sb.RecordUnsuccessfulPoll()
-
-	sb.RecordPoll(alphaConfidence, Blue)
-
-	require.Equal(Blue, sb.Preference())
-	require.False(sb.Finalized())
-
-	sb.RecordPoll(alphaConfidence, Blue)
-
-	require.Equal(Blue, sb.Preference())
-	require.True(sb.Finalized())
-
-	expected := "SB(Preference = TtF4d2QWbk5vzQGTEPrN48x6vwgAoAmKQ9cbp79inpQmcRKES, PreferenceStrength = 3, SF(Confidence = [2], Finalized = true, SL(Preference = TtF4d2QWbk5vzQGTEPrN48x6vwgAoAmKQ9cbp79inpQmcRKES)))"
-	require.Equal(expected, sb.String())
-
-	for i := 0; i < 4; i++ {
-		sb.RecordPoll(alphaConfidence, Red)
-
-		require.Equal(Blue, sb.Preference())
-		require.True(sb.Finalized())
-	}
-}
-
-func TestNarySnowballDifferentSnowflakeColor(t *testing.T) {
-	require := require.New(t)
-
-	alphaPreference, alphaConfidence := 1, 2
-	beta := 2
-	terminationConditions := newSingleTerminationCondition(alphaConfidence, beta)
-
-	sb := newNnarySnowball(alphaPreference, terminationConditions, Red)
-	sb.Add(Blue)
-
-	require.Equal(Red, sb.Preference())
-	require.False(sb.Finalized())
-
-	sb.RecordPoll(alphaConfidence, Blue)
-
-	require.Equal(Blue, sb.nnarySnowflake.Preference())
-
-	sb.RecordPoll(alphaConfidence, Red)
-
-	require.Equal(Blue, sb.Preference())
-	require.Equal(Red, sb.nnarySnowflake.Preference())
-}
diff --git a/snow/consensus/snowball/tree.go b/snow/consensus/snowball/tree.go
index c6773e30c54e..a11b92e1fd03 100644
--- a/snow/consensus/snowball/tree.go
+++ b/snow/consensus/snowball/tree.go
@@ -360,7 +360,7 @@ func (u *unaryNode) Add(newChoice ids.ID) node {
 	newChild := &unaryNode{
 		tree:          u.tree,
 		preference:    newChoice,
-		decidedPrefix: index + 1,   // The new child assumes this branch has decided in it's favor
+		decidedPrefix: index + 1,   // The new child assumes this branch has decided in its favor
 		commonPrefix:  ids.NumBits, // The new child has no conflicts under this branch
 		snow:          newChildSnow,
 	}
diff --git a/snow/consensus/snowball/tree_test.go b/snow/consensus/snowball/tree_test.go
index fc9c8944b768..8095863afb10 100644
--- a/snow/consensus/snowball/tree_test.go
+++ b/snow/consensus/snowball/tree_test.go
@@ -15,7 +15,7 @@ import (
 	"github.com/ava-labs/avalanchego/utils/bag"
 )
 
-const initialUnaryDescription = "SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [0, 256)"
+const initialUnaryDescription = "SF(Confidence = [0], Finalized = false) Bits = [0, 256)"
 
 func TestSnowballSingleton(t *testing.T) {
 	require := require.New(t)
@@ -26,7 +26,7 @@ func TestSnowballSingleton(t *testing.T) {
 		AlphaConfidence: 1,
 		Beta:            2,
 	}
-	tree := NewTree(SnowballFactory, params, Red)
+	tree := NewTree(SnowflakeFactory, params, Red)
 
 	require.False(tree.Finalized())
 
@@ -66,7 +66,7 @@ func TestSnowballRecordUnsuccessfulPoll(t *testing.T) {
 		AlphaConfidence: 1,
 		Beta:            3,
 	}
-	tree := NewTree(SnowballFactory, params, Red)
+	tree := NewTree(SnowflakeFactory, params, Red)
 
 	require.False(tree.Finalized())
 
@@ -95,7 +95,7 @@ func TestSnowballBinary(t *testing.T) {
 		AlphaConfidence: 1,
 		Beta:            2,
 	}
-	tree := NewTree(SnowballFactory, params, Red)
+	tree := NewTree(SnowflakeFactory, params, Red)
 	tree.Add(Blue)
 
 	require.Equal(Red, tree.Preference())
@@ -108,7 +108,7 @@ func TestSnowballBinary(t *testing.T) {
 
 	oneRed := bag.Of(Red)
 	require.True(tree.RecordPoll(oneRed))
-	require.Equal(Blue, tree.Preference())
+	require.Equal(Red, tree.Preference())
 	require.False(tree.Finalized())
 
 	require.True(tree.RecordPoll(oneBlue))
@@ -137,14 +137,14 @@ func TestSnowballLastBinary(t *testing.T) {
 		AlphaConfidence: 1,
 		Beta:            2,
 	}
-	tree := NewTree(SnowballFactory, params, zero)
+	tree := NewTree(SnowflakeFactory, params, zero)
 	tree.Add(one)
 
 	// Should do nothing
 	tree.Add(one)
 
-	expected := `SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [0, 255)
-    SB(Preference = 0, PreferenceStrength[0] = 0, PreferenceStrength[1] = 0, SF(Confidence = [0], Finalized = false, SL(Preference = 0))) Bit = 255`
+	expected := `SF(Confidence = [0], Finalized = false) Bits = [0, 255)
+    SF(Confidence = [0], Finalized = false, SL(Preference = 0)) Bit = 255`
 	require.Equal(expected, tree.String())
 	require.Equal(zero, tree.Preference())
 	require.False(tree.Finalized())
@@ -154,15 +154,15 @@ func TestSnowballLastBinary(t *testing.T) {
 	require.Equal(one, tree.Preference())
 	require.False(tree.Finalized())
 
-	expected = `SB(PreferenceStrength = 1, SF(Confidence = [1], Finalized = false)) Bits = [0, 255)
-    SB(Preference = 1, PreferenceStrength[0] = 0, PreferenceStrength[1] = 1, SF(Confidence = [1], Finalized = false, SL(Preference = 1))) Bit = 255`
+	expected = `SF(Confidence = [1], Finalized = false) Bits = [0, 255)
+    SF(Confidence = [1], Finalized = false, SL(Preference = 1)) Bit = 255`
 	require.Equal(expected, tree.String())
 
 	require.True(tree.RecordPoll(oneBag))
 	require.Equal(one, tree.Preference())
 	require.True(tree.Finalized())
 
-	expected = "SB(Preference = 1, PreferenceStrength[0] = 0, PreferenceStrength[1] = 2, SF(Confidence = [2], Finalized = true, SL(Preference = 1))) Bit = 255"
+	expected = "SF(Confidence = [2], Finalized = true, SL(Preference = 1)) Bit = 255"
 	require.Equal(expected, tree.String())
 }
 
@@ -178,12 +178,12 @@ func TestSnowballFirstBinary(t *testing.T) {
 		AlphaConfidence: 1,
 		Beta:            2,
 	}
-	tree := NewTree(SnowballFactory, params, zero)
+	tree := NewTree(SnowflakeFactory, params, zero)
 	tree.Add(one)
 
-	expected := `SB(Preference = 0, PreferenceStrength[0] = 0, PreferenceStrength[1] = 0, SF(Confidence = [0], Finalized = false, SL(Preference = 0))) Bit = 0
-    SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [1, 256)
-    SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [1, 256)`
+	expected := `SF(Confidence = [0], Finalized = false, SL(Preference = 0)) Bit = 0
+    SF(Confidence = [0], Finalized = false) Bits = [1, 256)
+    SF(Confidence = [0], Finalized = false) Bits = [1, 256)`
 	require.Equal(expected, tree.String())
 	require.Equal(zero, tree.Preference())
 	require.False(tree.Finalized())
@@ -193,16 +193,16 @@ func TestSnowballFirstBinary(t *testing.T) {
 	require.Equal(one, tree.Preference())
 	require.False(tree.Finalized())
 
-	expected = `SB(Preference = 1, PreferenceStrength[0] = 0, PreferenceStrength[1] = 1, SF(Confidence = [1], Finalized = false, SL(Preference = 1))) Bit = 0
-    SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [1, 256)
-    SB(PreferenceStrength = 1, SF(Confidence = [1], Finalized = false)) Bits = [1, 256)`
+	expected = `SF(Confidence = [1], Finalized = false, SL(Preference = 1)) Bit = 0
+    SF(Confidence = [0], Finalized = false) Bits = [1, 256)
+    SF(Confidence = [1], Finalized = false) Bits = [1, 256)`
 	require.Equal(expected, tree.String())
 
 	require.True(tree.RecordPoll(oneBag))
 	require.Equal(one, tree.Preference())
 	require.True(tree.Finalized())
 
-	expected = `SB(PreferenceStrength = 2, SF(Confidence = [2], Finalized = true)) Bits = [1, 256)`
+	expected = `SF(Confidence = [2], Finalized = true) Bits = [1, 256)`
 	require.Equal(expected, tree.String())
 }
 
@@ -220,15 +220,15 @@ func TestSnowballAddDecidedFirstBit(t *testing.T) {
 		AlphaConfidence: 1,
 		Beta:            2,
 	}
-	tree := NewTree(SnowballFactory, params, zero)
+	tree := NewTree(SnowflakeFactory, params, zero)
 	tree.Add(c1000)
 	tree.Add(c1100)
 
-	expected := `SB(Preference = 0, PreferenceStrength[0] = 0, PreferenceStrength[1] = 0, SF(Confidence = [0], Finalized = false, SL(Preference = 0))) Bit = 0
-    SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [1, 256)
-    SB(Preference = 0, PreferenceStrength[0] = 0, PreferenceStrength[1] = 0, SF(Confidence = [0], Finalized = false, SL(Preference = 0))) Bit = 1
-        SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [2, 256)
-        SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [2, 256)`
+	expected := `SF(Confidence = [0], Finalized = false, SL(Preference = 0)) Bit = 0
+    SF(Confidence = [0], Finalized = false) Bits = [1, 256)
+    SF(Confidence = [0], Finalized = false, SL(Preference = 0)) Bit = 1
+        SF(Confidence = [0], Finalized = false) Bits = [2, 256)
+        SF(Confidence = [0], Finalized = false) Bits = [2, 256)`
 	require.Equal(expected, tree.String())
 	require.Equal(zero, tree.Preference())
 	require.False(tree.Finalized())
@@ -238,21 +238,21 @@ func TestSnowballAddDecidedFirstBit(t *testing.T) {
 	require.Equal(c1000, tree.Preference())
 	require.False(tree.Finalized())
 
-	expected = `SB(Preference = 1, PreferenceStrength[0] = 0, PreferenceStrength[1] = 1, SF(Confidence = [1], Finalized = false, SL(Preference = 1))) Bit = 0
-    SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [1, 256)
-    SB(Preference = 0, PreferenceStrength[0] = 1, PreferenceStrength[1] = 0, SF(Confidence = [1], Finalized = false, SL(Preference = 0))) Bit = 1
-        SB(PreferenceStrength = 1, SF(Confidence = [1], Finalized = false)) Bits = [2, 256)
-        SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [2, 256)`
+	expected = `SF(Confidence = [1], Finalized = false, SL(Preference = 1)) Bit = 0
+    SF(Confidence = [0], Finalized = false) Bits = [1, 256)
+    SF(Confidence = [1], Finalized = false, SL(Preference = 0)) Bit = 1
+        SF(Confidence = [1], Finalized = false) Bits = [2, 256)
+        SF(Confidence = [0], Finalized = false) Bits = [2, 256)`
 	require.Equal(expected, tree.String())
 
 	threeBag := bag.Of(c1100)
 	require.True(tree.RecordPoll(threeBag))
-	require.Equal(c1000, tree.Preference())
+	require.Equal(c1100, tree.Preference())
 	require.False(tree.Finalized())
 
-	expected = `SB(Preference = 0, PreferenceStrength[0] = 1, PreferenceStrength[1] = 1, SF(Confidence = [1], Finalized = false, SL(Preference = 1))) Bit = 1
-    SB(PreferenceStrength = 1, SF(Confidence = [1], Finalized = false)) Bits = [2, 256)
-    SB(PreferenceStrength = 1, SF(Confidence = [1], Finalized = false)) Bits = [2, 256)`
+	expected = `SF(Confidence = [1], Finalized = false, SL(Preference = 1)) Bit = 1
+    SF(Confidence = [1], Finalized = false) Bits = [2, 256)
+    SF(Confidence = [1], Finalized = false) Bits = [2, 256)`
 	require.Equal(expected, tree.String())
 
 	// Adding six should have no effect because the first bit is already decided
@@ -273,14 +273,14 @@ func TestSnowballAddPreviouslyRejected(t *testing.T) {
 		AlphaConfidence: 1,
 		Beta:            2,
 	}
-	tree := NewTree(SnowballFactory, params, zero)
+	tree := NewTree(SnowflakeFactory, params, zero)
 	tree.Add(two)
 
 	{
-		expected := `SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [0, 1)
-    SB(Preference = 0, PreferenceStrength[0] = 0, PreferenceStrength[1] = 0, SF(Confidence = [0], Finalized = false, SL(Preference = 0))) Bit = 1
-        SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [2, 256)
-        SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [2, 256)`
+		expected := `SF(Confidence = [0], Finalized = false) Bits = [0, 1)
+    SF(Confidence = [0], Finalized = false, SL(Preference = 0)) Bit = 1
+        SF(Confidence = [0], Finalized = false) Bits = [2, 256)
+        SF(Confidence = [0], Finalized = false) Bits = [2, 256)`
 		require.Equal(expected, tree.String())
 		require.Equal(zero, tree.Preference())
 		require.False(tree.Finalized())
@@ -290,10 +290,10 @@ func TestSnowballAddPreviouslyRejected(t *testing.T) {
 	require.True(tree.RecordPoll(zeroBag))
 
 	{
-		expected := `SB(PreferenceStrength = 1, SF(Confidence = [1], Finalized = false)) Bits = [0, 1)
-    SB(Preference = 0, PreferenceStrength[0] = 1, PreferenceStrength[1] = 0, SF(Confidence = [1], Finalized = false, SL(Preference = 0))) Bit = 1
-        SB(PreferenceStrength = 1, SF(Confidence = [1], Finalized = false)) Bits = [2, 256)
-        SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [2, 256)`
+		expected := `SF(Confidence = [1], Finalized = false) Bits = [0, 1)
+    SF(Confidence = [1], Finalized = false, SL(Preference = 0)) Bit = 1
+        SF(Confidence = [1], Finalized = false) Bits = [2, 256)
+        SF(Confidence = [0], Finalized = false) Bits = [2, 256)`
 		require.Equal(expected, tree.String())
 		require.Equal(zero, tree.Preference())
 		require.False(tree.Finalized())
@@ -303,22 +303,22 @@ func TestSnowballAddPreviouslyRejected(t *testing.T) {
 	require.True(tree.RecordPoll(twoBag))
 
 	{
-		expected := `SB(Preference = 0, PreferenceStrength[0] = 1, PreferenceStrength[1] = 1, SF(Confidence = [1], Finalized = false, SL(Preference = 1))) Bit = 1
-    SB(PreferenceStrength = 1, SF(Confidence = [1], Finalized = false)) Bits = [2, 256)
-    SB(PreferenceStrength = 1, SF(Confidence = [1], Finalized = false)) Bits = [2, 256)`
+		expected := `SF(Confidence = [1], Finalized = false, SL(Preference = 1)) Bit = 1
+    SF(Confidence = [1], Finalized = false) Bits = [2, 256)
+    SF(Confidence = [1], Finalized = false) Bits = [2, 256)`
 		require.Equal(expected, tree.String())
-		require.Equal(zero, tree.Preference())
+		require.Equal(two, tree.Preference())
 		require.False(tree.Finalized())
 	}
 
 	tree.Add(one)
 
 	{
-		expected := `SB(Preference = 0, PreferenceStrength[0] = 1, PreferenceStrength[1] = 1, SF(Confidence = [1], Finalized = false, SL(Preference = 1))) Bit = 1
-    SB(PreferenceStrength = 1, SF(Confidence = [1], Finalized = false)) Bits = [2, 256)
-    SB(PreferenceStrength = 1, SF(Confidence = [1], Finalized = false)) Bits = [2, 256)`
+		expected := `SF(Confidence = [1], Finalized = false, SL(Preference = 1)) Bit = 1
+    SF(Confidence = [1], Finalized = false) Bits = [2, 256)
+    SF(Confidence = [1], Finalized = false) Bits = [2, 256)`
 		require.Equal(expected, tree.String())
-		require.Equal(zero, tree.Preference())
+		require.Equal(two, tree.Preference())
 		require.False(tree.Finalized())
 	}
 }
@@ -335,13 +335,13 @@ func TestSnowballNewUnary(t *testing.T) {
 		AlphaConfidence: 1,
 		Beta:            3,
 	}
-	tree := NewTree(SnowballFactory, params, zero)
+	tree := NewTree(SnowflakeFactory, params, zero)
 	tree.Add(one)
 
 	{
-		expected := `SB(Preference = 0, PreferenceStrength[0] = 0, PreferenceStrength[1] = 0, SF(Confidence = [0], Finalized = false, SL(Preference = 0))) Bit = 0
-    SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [1, 256)
-    SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [1, 256)`
+		expected := `SF(Confidence = [0], Finalized = false, SL(Preference = 0)) Bit = 0
+    SF(Confidence = [0], Finalized = false) Bits = [1, 256)
+    SF(Confidence = [0], Finalized = false) Bits = [1, 256)`
 		require.Equal(expected, tree.String())
 		require.Equal(zero, tree.Preference())
 		require.False(tree.Finalized())
@@ -351,9 +351,9 @@ func TestSnowballNewUnary(t *testing.T) {
 	require.True(tree.RecordPoll(oneBag))
 
 	{
-		expected := `SB(Preference = 1, PreferenceStrength[0] = 0, PreferenceStrength[1] = 1, SF(Confidence = [1], Finalized = false, SL(Preference = 1))) Bit = 0
-    SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [1, 256)
-    SB(PreferenceStrength = 1, SF(Confidence = [1], Finalized = false)) Bits = [1, 256)`
+		expected := `SF(Confidence = [1], Finalized = false, SL(Preference = 1)) Bit = 0
+    SF(Confidence = [0], Finalized = false) Bits = [1, 256)
+    SF(Confidence = [1], Finalized = false) Bits = [1, 256)`
 		require.Equal(expected, tree.String())
 		require.Equal(one, tree.Preference())
 		require.False(tree.Finalized())
@@ -362,9 +362,9 @@ func TestSnowballNewUnary(t *testing.T) {
 	require.True(tree.RecordPoll(oneBag))
 
 	{
-		expected := `SB(Preference = 1, PreferenceStrength[0] = 0, PreferenceStrength[1] = 2, SF(Confidence = [2], Finalized = false, SL(Preference = 1))) Bit = 0
-    SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [1, 256)
-    SB(PreferenceStrength = 2, SF(Confidence = [2], Finalized = false)) Bits = [1, 256)`
+		expected := `SF(Confidence = [2], Finalized = false, SL(Preference = 1)) Bit = 0
+    SF(Confidence = [0], Finalized = false) Bits = [1, 256)
+    SF(Confidence = [2], Finalized = false) Bits = [1, 256)`
 		require.Equal(expected, tree.String())
 		require.Equal(one, tree.Preference())
 		require.False(tree.Finalized())
@@ -384,18 +384,18 @@ func TestSnowballTransitiveReset(t *testing.T) {
 		AlphaConfidence: 1,
 		Beta:            2,
 	}
-	tree := NewTree(SnowballFactory, params, zero)
+	tree := NewTree(SnowflakeFactory, params, zero)
 	tree.Add(two)
 	tree.Add(eight)
 
 	{
-		expected := `SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [0, 1)
-    SB(Preference = 0, PreferenceStrength[0] = 0, PreferenceStrength[1] = 0, SF(Confidence = [0], Finalized = false, SL(Preference = 0))) Bit = 1
-        SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [2, 3)
-            SB(Preference = 0, PreferenceStrength[0] = 0, PreferenceStrength[1] = 0, SF(Confidence = [0], Finalized = false, SL(Preference = 0))) Bit = 3
-                SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [4, 256)
-                SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [4, 256)
-        SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [2, 256)`
+		expected := `SF(Confidence = [0], Finalized = false) Bits = [0, 1)
+    SF(Confidence = [0], Finalized = false, SL(Preference = 0)) Bit = 1
+        SF(Confidence = [0], Finalized = false) Bits = [2, 3)
+            SF(Confidence = [0], Finalized = false, SL(Preference = 0)) Bit = 3
+                SF(Confidence = [0], Finalized = false) Bits = [4, 256)
+                SF(Confidence = [0], Finalized = false) Bits = [4, 256)
+        SF(Confidence = [0], Finalized = false) Bits = [2, 256)`
 		require.Equal(expected, tree.String())
 		require.Equal(zero, tree.Preference())
 		require.False(tree.Finalized())
@@ -405,13 +405,13 @@ func TestSnowballTransitiveReset(t *testing.T) {
 	require.True(tree.RecordPoll(zeroBag))
 
 	{
-		expected := `SB(PreferenceStrength = 1, SF(Confidence = [1], Finalized = false)) Bits = [0, 1)
-    SB(Preference = 0, PreferenceStrength[0] = 1, PreferenceStrength[1] = 0, SF(Confidence = [1], Finalized = false, SL(Preference = 0))) Bit = 1
-        SB(PreferenceStrength = 1, SF(Confidence = [1], Finalized = false)) Bits = [2, 3)
-            SB(Preference = 0, PreferenceStrength[0] = 1, PreferenceStrength[1] = 0, SF(Confidence = [1], Finalized = false, SL(Preference = 0))) Bit = 3
-                SB(PreferenceStrength = 1, SF(Confidence = [1], Finalized = false)) Bits = [4, 256)
-                SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [4, 256)
-        SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [2, 256)`
+		expected := `SF(Confidence = [1], Finalized = false) Bits = [0, 1)
+    SF(Confidence = [1], Finalized = false, SL(Preference = 0)) Bit = 1
+        SF(Confidence = [1], Finalized = false) Bits = [2, 3)
+            SF(Confidence = [1], Finalized = false, SL(Preference = 0)) Bit = 3
+                SF(Confidence = [1], Finalized = false) Bits = [4, 256)
+                SF(Confidence = [0], Finalized = false) Bits = [4, 256)
+        SF(Confidence = [0], Finalized = false) Bits = [2, 256)`
 		require.Equal(expected, tree.String())
 		require.Equal(zero, tree.Preference())
 		require.False(tree.Finalized())
@@ -421,13 +421,13 @@ func TestSnowballTransitiveReset(t *testing.T) {
 	require.False(tree.RecordPoll(emptyBag))
 
 	{
-		expected := `SB(PreferenceStrength = 1, SF(Confidence = [0], Finalized = false)) Bits = [0, 1)
-    SB(Preference = 0, PreferenceStrength[0] = 1, PreferenceStrength[1] = 0, SF(Confidence = [1], Finalized = false, SL(Preference = 0))) Bit = 1
-        SB(PreferenceStrength = 1, SF(Confidence = [1], Finalized = false)) Bits = [2, 3)
-            SB(Preference = 0, PreferenceStrength[0] = 1, PreferenceStrength[1] = 0, SF(Confidence = [1], Finalized = false, SL(Preference = 0))) Bit = 3
-                SB(PreferenceStrength = 1, SF(Confidence = [1], Finalized = false)) Bits = [4, 256)
-                SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [4, 256)
-        SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [2, 256)`
+		expected := `SF(Confidence = [0], Finalized = false) Bits = [0, 1)
+    SF(Confidence = [1], Finalized = false, SL(Preference = 0)) Bit = 1
+        SF(Confidence = [1], Finalized = false) Bits = [2, 3)
+            SF(Confidence = [1], Finalized = false, SL(Preference = 0)) Bit = 3
+                SF(Confidence = [1], Finalized = false) Bits = [4, 256)
+                SF(Confidence = [0], Finalized = false) Bits = [4, 256)
+        SF(Confidence = [0], Finalized = false) Bits = [2, 256)`
 		require.Equal(expected, tree.String())
 		require.Equal(zero, tree.Preference())
 		require.False(tree.Finalized())
@@ -436,13 +436,13 @@ func TestSnowballTransitiveReset(t *testing.T) {
 	require.True(tree.RecordPoll(zeroBag))
 
 	{
-		expected := `SB(PreferenceStrength = 2, SF(Confidence = [1], Finalized = false)) Bits = [0, 1)
-    SB(Preference = 0, PreferenceStrength[0] = 2, PreferenceStrength[1] = 0, SF(Confidence = [1], Finalized = false, SL(Preference = 0))) Bit = 1
-        SB(PreferenceStrength = 2, SF(Confidence = [1], Finalized = false)) Bits = [2, 3)
-            SB(Preference = 0, PreferenceStrength[0] = 2, PreferenceStrength[1] = 0, SF(Confidence = [1], Finalized = false, SL(Preference = 0))) Bit = 3
-                SB(PreferenceStrength = 2, SF(Confidence = [1], Finalized = false)) Bits = [4, 256)
-                SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [4, 256)
-        SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [2, 256)`
+		expected := `SF(Confidence = [1], Finalized = false) Bits = [0, 1)
+    SF(Confidence = [1], Finalized = false, SL(Preference = 0)) Bit = 1
+        SF(Confidence = [1], Finalized = false) Bits = [2, 3)
+            SF(Confidence = [1], Finalized = false, SL(Preference = 0)) Bit = 3
+                SF(Confidence = [1], Finalized = false) Bits = [4, 256)
+                SF(Confidence = [0], Finalized = false) Bits = [4, 256)
+        SF(Confidence = [0], Finalized = false) Bits = [2, 256)`
 		require.Equal(expected, tree.String())
 		require.Equal(zero, tree.Preference())
 		require.False(tree.Finalized())
@@ -451,7 +451,7 @@ func TestSnowballTransitiveReset(t *testing.T) {
 	require.True(tree.RecordPoll(zeroBag))
 
 	{
-		expected := "SB(PreferenceStrength = 3, SF(Confidence = [2], Finalized = true)) Bits = [4, 256)"
+		expected := "SF(Confidence = [2], Finalized = true) Bits = [4, 256)"
 		require.Equal(expected, tree.String())
 		require.Equal(zero, tree.Preference())
 		require.True(tree.Finalized())
@@ -467,7 +467,7 @@ func TestSnowballTrinary(t *testing.T) {
 		AlphaConfidence: 1,
 		Beta:            2,
 	}
-	tree := NewTree(SnowballFactory, params, Green)
+	tree := NewTree(SnowflakeFactory, params, Green)
 	tree.Add(Red)
 	tree.Add(Blue)
 
@@ -485,23 +485,44 @@ func TestSnowballTrinary(t *testing.T) {
 	require.Equal(Red, tree.Preference())
 	require.False(tree.Finalized())
 
+	//       *
+	//     1/ \
+	//     R   *
+	//        / \
+	//       G   B
+
 	blueBag := bag.Of(Blue)
 	require.True(tree.RecordPoll(blueBag))
-	require.Equal(Red, tree.Preference())
+	require.Equal(Blue, tree.Preference())
 	require.False(tree.Finalized())
 
-	// Here is a case where voting for a color makes a different color become
-	// the preferred color. This is intended behavior.
+	//       *
+	//     1/ \1
+	//     R   *
+	//        / \1
+	//       G   B
+
 	greenBag := bag.Of(Green)
 	require.True(tree.RecordPoll(greenBag))
-	require.Equal(Blue, tree.Preference())
+	require.Equal(Green, tree.Preference())
 	require.False(tree.Finalized())
 
+	//       *
+	//     1/ \2
+	//     R   *
+	//       1/ \1
+	//       G   B
+
 	// Red has already been rejected here, so this is not a successful poll.
 	require.False(tree.RecordPoll(redBag))
-	require.Equal(Blue, tree.Preference())
+	require.Equal(Green, tree.Preference())
 	require.False(tree.Finalized())
 
+	//       *
+	//     1/ \3
+	//     R   *
+	//       2/ \1
+	//       G   B
 	require.True(tree.RecordPoll(greenBag))
 	require.Equal(Green, tree.Preference())
 	require.False(tree.Finalized())
@@ -520,7 +541,7 @@ func TestSnowballCloseTrinary(t *testing.T) {
 		AlphaConfidence: 1,
 		Beta:            2,
 	}
-	tree := NewTree(SnowballFactory, params, yellow)
+	tree := NewTree(SnowflakeFactory, params, yellow)
 	tree.Add(cyan)
 	tree.Add(magenta)
 
@@ -538,19 +559,37 @@ func TestSnowballCloseTrinary(t *testing.T) {
 	require.Equal(yellow, tree.Preference())
 	require.False(tree.Finalized())
 
+	//       *
+	//      / \1
+	//     C   *
+	//       1/ \
+	//       Y   M
+
 	magentaBag := bag.Of(magenta)
 	require.True(tree.RecordPoll(magentaBag))
-	require.Equal(yellow, tree.Preference())
+	require.Equal(magenta, tree.Preference())
 	require.False(tree.Finalized())
 
+	//       *
+	//      / \2
+	//     C   *
+	//       1/ \1
+	//       Y   M
+
 	// Cyan has already been rejected here, so these are not successful polls.
 	cyanBag := bag.Of(cyan)
 	require.False(tree.RecordPoll(cyanBag))
-	require.Equal(yellow, tree.Preference())
+	require.Equal(magenta, tree.Preference())
 	require.False(tree.Finalized())
 
+	//       *
+	//      / \2
+	//     C   *
+	//       1/ \1
+	//       Y   M
+
 	require.False(tree.RecordPoll(cyanBag))
-	require.Equal(yellow, tree.Preference())
+	require.Equal(magenta, tree.Preference())
 	require.False(tree.Finalized())
 }
 
@@ -567,7 +606,7 @@ func TestSnowballResetChild(t *testing.T) {
 		AlphaConfidence: 1,
 		Beta:            2,
 	}
-	tree := NewTree(SnowballFactory, params, c0000)
+	tree := NewTree(SnowflakeFactory, params, c0000)
 	tree.Add(c0100)
 	tree.Add(c1000)
 
@@ -578,11 +617,11 @@ func TestSnowballResetChild(t *testing.T) {
 	require.True(tree.RecordPoll(c0000Bag))
 
 	{
-		expected := `SB(Preference = 0, PreferenceStrength[0] = 1, PreferenceStrength[1] = 0, SF(Confidence = [1], Finalized = false, SL(Preference = 0))) Bit = 0
-    SB(Preference = 0, PreferenceStrength[0] = 1, PreferenceStrength[1] = 0, SF(Confidence = [1], Finalized = false, SL(Preference = 0))) Bit = 1
-        SB(PreferenceStrength = 1, SF(Confidence = [1], Finalized = false)) Bits = [2, 256)
-        SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [2, 256)
-    SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [1, 256)`
+		expected := `SF(Confidence = [1], Finalized = false, SL(Preference = 0)) Bit = 0
+    SF(Confidence = [1], Finalized = false, SL(Preference = 0)) Bit = 1
+        SF(Confidence = [1], Finalized = false) Bits = [2, 256)
+        SF(Confidence = [0], Finalized = false) Bits = [2, 256)
+    SF(Confidence = [0], Finalized = false) Bits = [1, 256)`
 		require.Equal(expected, tree.String())
 		require.Equal(c0000, tree.Preference())
 		require.False(tree.Finalized())
@@ -592,11 +631,11 @@ func TestSnowballResetChild(t *testing.T) {
 	require.False(tree.RecordPoll(emptyBag))
 
 	{
-		expected := `SB(Preference = 0, PreferenceStrength[0] = 1, PreferenceStrength[1] = 0, SF(Confidence = [0], Finalized = false, SL(Preference = 0))) Bit = 0
-    SB(Preference = 0, PreferenceStrength[0] = 1, PreferenceStrength[1] = 0, SF(Confidence = [1], Finalized = false, SL(Preference = 0))) Bit = 1
-        SB(PreferenceStrength = 1, SF(Confidence = [1], Finalized = false)) Bits = [2, 256)
-        SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [2, 256)
-    SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [1, 256)`
+		expected := `SF(Confidence = [0], Finalized = false, SL(Preference = 0)) Bit = 0
+    SF(Confidence = [1], Finalized = false, SL(Preference = 0)) Bit = 1
+        SF(Confidence = [1], Finalized = false) Bits = [2, 256)
+        SF(Confidence = [0], Finalized = false) Bits = [2, 256)
+    SF(Confidence = [0], Finalized = false) Bits = [1, 256)`
 		require.Equal(expected, tree.String())
 		require.Equal(c0000, tree.Preference())
 		require.False(tree.Finalized())
@@ -605,11 +644,11 @@ func TestSnowballResetChild(t *testing.T) {
 	require.True(tree.RecordPoll(c0000Bag))
 
 	{
-		expected := `SB(Preference = 0, PreferenceStrength[0] = 2, PreferenceStrength[1] = 0, SF(Confidence = [1], Finalized = false, SL(Preference = 0))) Bit = 0
-    SB(Preference = 0, PreferenceStrength[0] = 2, PreferenceStrength[1] = 0, SF(Confidence = [1], Finalized = false, SL(Preference = 0))) Bit = 1
-        SB(PreferenceStrength = 2, SF(Confidence = [1], Finalized = false)) Bits = [2, 256)
-        SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [2, 256)
-    SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [1, 256)`
+		expected := `SF(Confidence = [1], Finalized = false, SL(Preference = 0)) Bit = 0
+    SF(Confidence = [1], Finalized = false, SL(Preference = 0)) Bit = 1
+        SF(Confidence = [1], Finalized = false) Bits = [2, 256)
+        SF(Confidence = [0], Finalized = false) Bits = [2, 256)
+    SF(Confidence = [0], Finalized = false) Bits = [1, 256)`
 		require.Equal(expected, tree.String())
 		require.Equal(c0000, tree.Preference())
 		require.False(tree.Finalized())
@@ -629,7 +668,7 @@ func TestSnowballResetSibling(t *testing.T) {
 		AlphaConfidence: 1,
 		Beta:            2,
 	}
-	tree := NewTree(SnowballFactory, params, c0000)
+	tree := NewTree(SnowflakeFactory, params, c0000)
 	tree.Add(c0100)
 	tree.Add(c1000)
 
@@ -640,11 +679,11 @@ func TestSnowballResetSibling(t *testing.T) {
 	require.True(tree.RecordPoll(c0100Bag))
 
 	{
-		expected := `SB(Preference = 0, PreferenceStrength[0] = 1, PreferenceStrength[1] = 0, SF(Confidence = [1], Finalized = false, SL(Preference = 0))) Bit = 0
-    SB(Preference = 1, PreferenceStrength[0] = 0, PreferenceStrength[1] = 1, SF(Confidence = [1], Finalized = false, SL(Preference = 1))) Bit = 1
-        SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [2, 256)
-        SB(PreferenceStrength = 1, SF(Confidence = [1], Finalized = false)) Bits = [2, 256)
-    SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [1, 256)`
+		expected := `SF(Confidence = [1], Finalized = false, SL(Preference = 0)) Bit = 0
+    SF(Confidence = [1], Finalized = false, SL(Preference = 1)) Bit = 1
+        SF(Confidence = [0], Finalized = false) Bits = [2, 256)
+        SF(Confidence = [1], Finalized = false) Bits = [2, 256)
+    SF(Confidence = [0], Finalized = false) Bits = [1, 256)`
 		require.Equal(expected, tree.String())
 		require.Equal(c0100, tree.Preference())
 		require.False(tree.Finalized())
@@ -654,24 +693,24 @@ func TestSnowballResetSibling(t *testing.T) {
 	require.True(tree.RecordPoll(c1000Bag))
 
 	{
-		expected := `SB(Preference = 0, PreferenceStrength[0] = 1, PreferenceStrength[1] = 1, SF(Confidence = [1], Finalized = false, SL(Preference = 1))) Bit = 0
-    SB(Preference = 1, PreferenceStrength[0] = 0, PreferenceStrength[1] = 1, SF(Confidence = [1], Finalized = false, SL(Preference = 1))) Bit = 1
-        SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [2, 256)
-        SB(PreferenceStrength = 1, SF(Confidence = [1], Finalized = false)) Bits = [2, 256)
-    SB(PreferenceStrength = 1, SF(Confidence = [1], Finalized = false)) Bits = [1, 256)`
+		expected := `SF(Confidence = [1], Finalized = false, SL(Preference = 1)) Bit = 0
+    SF(Confidence = [1], Finalized = false, SL(Preference = 1)) Bit = 1
+        SF(Confidence = [0], Finalized = false) Bits = [2, 256)
+        SF(Confidence = [1], Finalized = false) Bits = [2, 256)
+    SF(Confidence = [1], Finalized = false) Bits = [1, 256)`
 		require.Equal(expected, tree.String())
-		require.Equal(c0100, tree.Preference())
+		require.Equal(c1000, tree.Preference())
 		require.False(tree.Finalized())
 	}
 
 	require.True(tree.RecordPoll(c0100Bag))
 
 	{
-		expected := `SB(Preference = 0, PreferenceStrength[0] = 2, PreferenceStrength[1] = 1, SF(Confidence = [1], Finalized = false, SL(Preference = 0))) Bit = 0
-    SB(Preference = 1, PreferenceStrength[0] = 0, PreferenceStrength[1] = 2, SF(Confidence = [1], Finalized = false, SL(Preference = 1))) Bit = 1
-        SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [2, 256)
-        SB(PreferenceStrength = 2, SF(Confidence = [1], Finalized = false)) Bits = [2, 256)
-    SB(PreferenceStrength = 1, SF(Confidence = [1], Finalized = false)) Bits = [1, 256)`
+		expected := `SF(Confidence = [1], Finalized = false, SL(Preference = 0)) Bit = 0
+    SF(Confidence = [1], Finalized = false, SL(Preference = 1)) Bit = 1
+        SF(Confidence = [0], Finalized = false) Bits = [2, 256)
+        SF(Confidence = [1], Finalized = false) Bits = [2, 256)
+    SF(Confidence = [1], Finalized = false) Bits = [1, 256)`
 		require.Equal(expected, tree.String())
 		require.Equal(c0100, tree.Preference())
 		require.False(tree.Finalized())
@@ -694,14 +733,14 @@ func TestSnowball5Colors(t *testing.T) {
 		colors = append(colors, ids.Empty.Prefix(uint64(i)))
 	}
 
-	tree0 := NewTree(SnowballFactory, params, colors[4])
+	tree0 := NewTree(SnowflakeFactory, params, colors[4])
 
 	tree0.Add(colors[0])
 	tree0.Add(colors[1])
 	tree0.Add(colors[2])
 	tree0.Add(colors[3])
 
-	tree1 := NewTree(SnowballFactory, params, colors[3])
+	tree1 := NewTree(SnowflakeFactory, params, colors[3])
 
 	tree1.Add(colors[0])
 	tree1.Add(colors[1])
@@ -727,7 +766,7 @@ func TestSnowballFineGrained(t *testing.T) {
 		AlphaConfidence: 1,
 		Beta:            2,
 	}
-	tree := NewTree(SnowballFactory, params, c0000)
+	tree := NewTree(SnowflakeFactory, params, c0000)
 
 	require.Equal(initialUnaryDescription, tree.String())
 	require.Equal(c0000, tree.Preference())
@@ -736,9 +775,9 @@ func TestSnowballFineGrained(t *testing.T) {
 	tree.Add(c1100)
 
 	{
-		expected := `SB(Preference = 0, PreferenceStrength[0] = 0, PreferenceStrength[1] = 0, SF(Confidence = [0], Finalized = false, SL(Preference = 0))) Bit = 0
-    SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [1, 256)
-    SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [1, 256)`
+		expected := `SF(Confidence = [0], Finalized = false, SL(Preference = 0)) Bit = 0
+    SF(Confidence = [0], Finalized = false) Bits = [1, 256)
+    SF(Confidence = [0], Finalized = false) Bits = [1, 256)`
 		require.Equal(expected, tree.String())
 		require.Equal(c0000, tree.Preference())
 		require.False(tree.Finalized())
@@ -747,11 +786,11 @@ func TestSnowballFineGrained(t *testing.T) {
 	tree.Add(c1000)
 
 	{
-		expected := `SB(Preference = 0, PreferenceStrength[0] = 0, PreferenceStrength[1] = 0, SF(Confidence = [0], Finalized = false, SL(Preference = 0))) Bit = 0
-    SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [1, 256)
-    SB(Preference = 1, PreferenceStrength[0] = 0, PreferenceStrength[1] = 0, SF(Confidence = [0], Finalized = false, SL(Preference = 1))) Bit = 1
-        SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [2, 256)
-        SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [2, 256)`
+		expected := `SF(Confidence = [0], Finalized = false, SL(Preference = 0)) Bit = 0
+    SF(Confidence = [0], Finalized = false) Bits = [1, 256)
+    SF(Confidence = [0], Finalized = false, SL(Preference = 1)) Bit = 1
+        SF(Confidence = [0], Finalized = false) Bits = [2, 256)
+        SF(Confidence = [0], Finalized = false) Bits = [2, 256)`
 		require.Equal(expected, tree.String())
 		require.Equal(c0000, tree.Preference())
 		require.False(tree.Finalized())
@@ -760,14 +799,14 @@ func TestSnowballFineGrained(t *testing.T) {
 	tree.Add(c0010)
 
 	{
-		expected := `SB(Preference = 0, PreferenceStrength[0] = 0, PreferenceStrength[1] = 0, SF(Confidence = [0], Finalized = false, SL(Preference = 0))) Bit = 0
-    SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [1, 2)
-        SB(Preference = 0, PreferenceStrength[0] = 0, PreferenceStrength[1] = 0, SF(Confidence = [0], Finalized = false, SL(Preference = 0))) Bit = 2
-            SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [3, 256)
-            SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [3, 256)
-    SB(Preference = 1, PreferenceStrength[0] = 0, PreferenceStrength[1] = 0, SF(Confidence = [0], Finalized = false, SL(Preference = 1))) Bit = 1
-        SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [2, 256)
-        SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [2, 256)`
+		expected := `SF(Confidence = [0], Finalized = false, SL(Preference = 0)) Bit = 0
+    SF(Confidence = [0], Finalized = false) Bits = [1, 2)
+        SF(Confidence = [0], Finalized = false, SL(Preference = 0)) Bit = 2
+            SF(Confidence = [0], Finalized = false) Bits = [3, 256)
+            SF(Confidence = [0], Finalized = false) Bits = [3, 256)
+    SF(Confidence = [0], Finalized = false, SL(Preference = 1)) Bit = 1
+        SF(Confidence = [0], Finalized = false) Bits = [2, 256)
+        SF(Confidence = [0], Finalized = false) Bits = [2, 256)`
 		require.Equal(expected, tree.String())
 		require.Equal(c0000, tree.Preference())
 		require.False(tree.Finalized())
@@ -777,14 +816,14 @@ func TestSnowballFineGrained(t *testing.T) {
 	require.True(tree.RecordPoll(c0000Bag))
 
 	{
-		expected := `SB(Preference = 0, PreferenceStrength[0] = 1, PreferenceStrength[1] = 0, SF(Confidence = [1], Finalized = false, SL(Preference = 0))) Bit = 0
-    SB(PreferenceStrength = 1, SF(Confidence = [1], Finalized = false)) Bits = [1, 2)
-        SB(Preference = 0, PreferenceStrength[0] = 1, PreferenceStrength[1] = 0, SF(Confidence = [1], Finalized = false, SL(Preference = 0))) Bit = 2
-            SB(PreferenceStrength = 1, SF(Confidence = [1], Finalized = false)) Bits = [3, 256)
-            SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [3, 256)
-    SB(Preference = 1, PreferenceStrength[0] = 0, PreferenceStrength[1] = 0, SF(Confidence = [0], Finalized = false, SL(Preference = 1))) Bit = 1
-        SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [2, 256)
-        SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [2, 256)`
+		expected := `SF(Confidence = [1], Finalized = false, SL(Preference = 0)) Bit = 0
+    SF(Confidence = [1], Finalized = false) Bits = [1, 2)
+        SF(Confidence = [1], Finalized = false, SL(Preference = 0)) Bit = 2
+            SF(Confidence = [1], Finalized = false) Bits = [3, 256)
+            SF(Confidence = [0], Finalized = false) Bits = [3, 256)
+    SF(Confidence = [0], Finalized = false, SL(Preference = 1)) Bit = 1
+        SF(Confidence = [0], Finalized = false) Bits = [2, 256)
+        SF(Confidence = [0], Finalized = false) Bits = [2, 256)`
 		require.Equal(expected, tree.String())
 		require.Equal(c0000, tree.Preference())
 		require.False(tree.Finalized())
@@ -794,17 +833,17 @@ func TestSnowballFineGrained(t *testing.T) {
 	require.True(tree.RecordPoll(c0010Bag))
 
 	{
-		expected := `SB(Preference = 0, PreferenceStrength[0] = 1, PreferenceStrength[1] = 1, SF(Confidence = [1], Finalized = false, SL(Preference = 1))) Bit = 2
-    SB(PreferenceStrength = 1, SF(Confidence = [1], Finalized = false)) Bits = [3, 256)
-    SB(PreferenceStrength = 1, SF(Confidence = [1], Finalized = false)) Bits = [3, 256)`
+		expected := `SF(Confidence = [1], Finalized = false, SL(Preference = 1)) Bit = 2
+    SF(Confidence = [1], Finalized = false) Bits = [3, 256)
+    SF(Confidence = [1], Finalized = false) Bits = [3, 256)`
 		require.Equal(expected, tree.String())
-		require.Equal(c0000, tree.Preference())
+		require.Equal(c0010, tree.Preference())
 		require.False(tree.Finalized())
 	}
 
 	require.True(tree.RecordPoll(c0010Bag))
 	{
-		expected := "SB(PreferenceStrength = 2, SF(Confidence = [2], Finalized = true)) Bits = [3, 256)"
+		expected := "SF(Confidence = [2], Finalized = true) Bits = [3, 256)"
 		require.Equal(expected, tree.String())
 		require.Equal(c0010, tree.Preference())
 		require.True(tree.Finalized())
@@ -820,7 +859,7 @@ func TestSnowballDoubleAdd(t *testing.T) {
 		AlphaConfidence: 1,
 		Beta:            3,
 	}
-	tree := NewTree(SnowballFactory, params, Red)
+	tree := NewTree(SnowflakeFactory, params, Red)
 	tree.Add(Red)
 
 	require.Equal(initialUnaryDescription, tree.String())
@@ -844,7 +883,7 @@ func TestSnowballConsistent(t *testing.T) {
 		source        = prng.NewMT19937()
 	)
 
-	n := NewNetwork(SnowballFactory, params, numColors, source)
+	n := NewNetwork(SnowflakeFactory, params, numColors, source)
 
 	source.Seed(seed)
 	for i := 0; i < numNodes; i++ {
@@ -872,7 +911,7 @@ func TestSnowballFilterBinaryChildren(t *testing.T) {
 		AlphaConfidence: 1,
 		Beta:            2,
 	}
-	tree := NewTree(SnowballFactory, params, c0000)
+	tree := NewTree(SnowflakeFactory, params, c0000)
 
 	require.Equal(initialUnaryDescription, tree.String())
 	require.Equal(c0000, tree.Preference())
@@ -881,9 +920,9 @@ func TestSnowballFilterBinaryChildren(t *testing.T) {
 	tree.Add(c1000)
 
 	{
-		expected := `SB(Preference = 0, PreferenceStrength[0] = 0, PreferenceStrength[1] = 0, SF(Confidence = [0], Finalized = false, SL(Preference = 0))) Bit = 0
-    SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [1, 256)
-    SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [1, 256)`
+		expected := `SF(Confidence = [0], Finalized = false, SL(Preference = 0)) Bit = 0
+    SF(Confidence = [0], Finalized = false) Bits = [1, 256)
+    SF(Confidence = [0], Finalized = false) Bits = [1, 256)`
 		require.Equal(expected, tree.String())
 		require.Equal(c0000, tree.Preference())
 		require.False(tree.Finalized())
@@ -892,12 +931,12 @@ func TestSnowballFilterBinaryChildren(t *testing.T) {
 	tree.Add(c0010)
 
 	{
-		expected := `SB(Preference = 0, PreferenceStrength[0] = 0, PreferenceStrength[1] = 0, SF(Confidence = [0], Finalized = false, SL(Preference = 0))) Bit = 0
-    SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [1, 2)
-        SB(Preference = 0, PreferenceStrength[0] = 0, PreferenceStrength[1] = 0, SF(Confidence = [0], Finalized = false, SL(Preference = 0))) Bit = 2
-            SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [3, 256)
-            SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [3, 256)
-    SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [1, 256)`
+		expected := `SF(Confidence = [0], Finalized = false, SL(Preference = 0)) Bit = 0
+    SF(Confidence = [0], Finalized = false) Bits = [1, 2)
+        SF(Confidence = [0], Finalized = false, SL(Preference = 0)) Bit = 2
+            SF(Confidence = [0], Finalized = false) Bits = [3, 256)
+            SF(Confidence = [0], Finalized = false) Bits = [3, 256)
+    SF(Confidence = [0], Finalized = false) Bits = [1, 256)`
 		require.Equal(expected, tree.String())
 		require.Equal(c0000, tree.Preference())
 		require.False(tree.Finalized())
@@ -907,12 +946,12 @@ func TestSnowballFilterBinaryChildren(t *testing.T) {
 	require.True(tree.RecordPoll(c0000Bag))
 
 	{
-		expected := `SB(Preference = 0, PreferenceStrength[0] = 1, PreferenceStrength[1] = 0, SF(Confidence = [1], Finalized = false, SL(Preference = 0))) Bit = 0
-    SB(PreferenceStrength = 1, SF(Confidence = [1], Finalized = false)) Bits = [1, 2)
-        SB(Preference = 0, PreferenceStrength[0] = 1, PreferenceStrength[1] = 0, SF(Confidence = [1], Finalized = false, SL(Preference = 0))) Bit = 2
-            SB(PreferenceStrength = 1, SF(Confidence = [1], Finalized = false)) Bits = [3, 256)
-            SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [3, 256)
-    SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [1, 256)`
+		expected := `SF(Confidence = [1], Finalized = false, SL(Preference = 0)) Bit = 0
+    SF(Confidence = [1], Finalized = false) Bits = [1, 2)
+        SF(Confidence = [1], Finalized = false, SL(Preference = 0)) Bit = 2
+            SF(Confidence = [1], Finalized = false) Bits = [3, 256)
+            SF(Confidence = [0], Finalized = false) Bits = [3, 256)
+    SF(Confidence = [0], Finalized = false) Bits = [1, 256)`
 		require.Equal(expected, tree.String())
 		require.Equal(c0000, tree.Preference())
 		require.False(tree.Finalized())
@@ -921,13 +960,13 @@ func TestSnowballFilterBinaryChildren(t *testing.T) {
 	tree.Add(c0100)
 
 	{
-		expected := `SB(Preference = 0, PreferenceStrength[0] = 1, PreferenceStrength[1] = 0, SF(Confidence = [1], Finalized = false, SL(Preference = 0))) Bit = 0
-    SB(Preference = 0, PreferenceStrength[0] = 1, PreferenceStrength[1] = 0, SF(Confidence = [1], Finalized = false, SL(Preference = 0))) Bit = 1
-        SB(Preference = 0, PreferenceStrength[0] = 1, PreferenceStrength[1] = 0, SF(Confidence = [1], Finalized = false, SL(Preference = 0))) Bit = 2
-            SB(PreferenceStrength = 1, SF(Confidence = [1], Finalized = false)) Bits = [3, 256)
-            SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [3, 256)
-        SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [2, 256)
-    SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [1, 256)`
+		expected := `SF(Confidence = [1], Finalized = false, SL(Preference = 0)) Bit = 0
+    SF(Confidence = [1], Finalized = false, SL(Preference = 0)) Bit = 1
+        SF(Confidence = [1], Finalized = false, SL(Preference = 0)) Bit = 2
+            SF(Confidence = [1], Finalized = false) Bits = [3, 256)
+            SF(Confidence = [0], Finalized = false) Bits = [3, 256)
+        SF(Confidence = [0], Finalized = false) Bits = [2, 256)
+    SF(Confidence = [0], Finalized = false) Bits = [1, 256)`
 		require.Equal(expected, tree.String())
 		require.Equal(c0000, tree.Preference())
 		require.False(tree.Finalized())
@@ -937,13 +976,13 @@ func TestSnowballFilterBinaryChildren(t *testing.T) {
 	require.True(tree.RecordPoll(c0100Bag))
 
 	{
-		expected := `SB(Preference = 0, PreferenceStrength[0] = 1, PreferenceStrength[1] = 1, SF(Confidence = [1], Finalized = false, SL(Preference = 1))) Bit = 1
-    SB(Preference = 0, PreferenceStrength[0] = 1, PreferenceStrength[1] = 0, SF(Confidence = [1], Finalized = false, SL(Preference = 0))) Bit = 2
-        SB(PreferenceStrength = 1, SF(Confidence = [1], Finalized = false)) Bits = [3, 256)
-        SB(PreferenceStrength = 0, SF(Confidence = [0], Finalized = false)) Bits = [3, 256)
-    SB(PreferenceStrength = 1, SF(Confidence = [1], Finalized = false)) Bits = [2, 256)`
+		expected := `SF(Confidence = [1], Finalized = false, SL(Preference = 1)) Bit = 1
+    SF(Confidence = [1], Finalized = false, SL(Preference = 0)) Bit = 2
+        SF(Confidence = [1], Finalized = false) Bits = [3, 256)
+        SF(Confidence = [0], Finalized = false) Bits = [3, 256)
+    SF(Confidence = [1], Finalized = false) Bits = [2, 256)`
 		require.Equal(expected, tree.String())
-		require.Equal(c0000, tree.Preference())
+		require.Equal(c0100, tree.Preference())
 		require.False(tree.Finalized())
 	}
 }
@@ -957,7 +996,7 @@ func TestSnowballRecordPreferencePollBinary(t *testing.T) {
 		AlphaConfidence: 3,
 		Beta:            2,
 	}
-	tree := NewTree(SnowballFactory, params, Red)
+	tree := NewTree(SnowflakeFactory, params, Red)
 	tree.Add(Blue)
 	require.Equal(Red, tree.Preference())
 	require.False(tree.Finalized())
@@ -969,7 +1008,7 @@ func TestSnowballRecordPreferencePollBinary(t *testing.T) {
 
 	twoRed := bag.Of(Red, Red)
 	require.True(tree.RecordPoll(twoRed))
-	require.Equal(Blue, tree.Preference())
+	require.Equal(Red, tree.Preference())
 	require.False(tree.Finalized())
 
 	threeRed := bag.Of(Red, Red, Red)
@@ -980,6 +1019,10 @@ func TestSnowballRecordPreferencePollBinary(t *testing.T) {
 	require.True(tree.RecordPoll(threeRed))
 	require.Equal(Red, tree.Preference())
 	require.True(tree.Finalized())
+
+	require.False(tree.RecordPoll(threeBlue))
+	require.Equal(Red, tree.Preference())
+	require.True(tree.Finalized())
 }
 
 func TestSnowballRecordPreferencePollUnary(t *testing.T) {
@@ -991,7 +1034,7 @@ func TestSnowballRecordPreferencePollUnary(t *testing.T) {
 		AlphaConfidence: 3,
 		Beta:            2,
 	}
-	tree := NewTree(SnowballFactory, params, Red)
+	tree := NewTree(SnowflakeFactory, params, Red)
 	require.Equal(Red, tree.Preference())
 	require.False(tree.Finalized())
 
@@ -1004,7 +1047,7 @@ func TestSnowballRecordPreferencePollUnary(t *testing.T) {
 
 	threeBlue := bag.Of(Blue, Blue, Blue)
 	require.True(tree.RecordPoll(threeBlue))
-	require.Equal(Red, tree.Preference())
+	require.Equal(Blue, tree.Preference())
 	require.False(tree.Finalized())
 
 	require.True(tree.RecordPoll(threeBlue))
diff --git a/snow/consensus/snowball/unary_snowball_test.go b/snow/consensus/snowball/unary_snowball_test.go
deleted file mode 100644
index 007d2ab53090..000000000000
--- a/snow/consensus/snowball/unary_snowball_test.go
+++ /dev/null
@@ -1,76 +0,0 @@
-// Copyright (C) 2019-2024, Ava Labs, Inc. All rights reserved.
-// See the file LICENSE for licensing terms.
-
-package snowball
-
-import (
-	"testing"
-
-	"github.com/stretchr/testify/require"
-)
-
-func UnarySnowballStateTest(t *testing.T, sb *unarySnowball, expectedPreferenceStrength int, expectedConfidence []int, expectedFinalized bool) {
-	require := require.New(t)
-
-	require.Equal(expectedPreferenceStrength, sb.preferenceStrength)
-	require.Equal(expectedConfidence, sb.confidence)
-	require.Equal(expectedFinalized, sb.Finalized())
-}
-
-func TestUnarySnowball(t *testing.T) {
-	require := require.New(t)
-
-	alphaPreference, alphaConfidence := 1, 2
-	beta := 2
-	terminationConditions := newSingleTerminationCondition(alphaConfidence, beta)
-
-	sb := newUnarySnowball(alphaPreference, terminationConditions)
-
-	sb.RecordPoll(alphaConfidence)
-	UnarySnowballStateTest(t, &sb, 1, []int{1}, false)
-
-	sb.RecordPoll(alphaPreference)
-	UnarySnowballStateTest(t, &sb, 2, []int{0}, false)
-
-	sb.RecordPoll(alphaConfidence)
-	UnarySnowballStateTest(t, &sb, 3, []int{1}, false)
-
-	sb.RecordUnsuccessfulPoll()
-	UnarySnowballStateTest(t, &sb, 3, []int{0}, false)
-
-	sb.RecordPoll(alphaConfidence)
-	UnarySnowballStateTest(t, &sb, 4, []int{1}, false)
-
-	sbCloneIntf := sb.Clone()
-	require.IsType(&unarySnowball{}, sbCloneIntf)
-	sbClone := sbCloneIntf.(*unarySnowball)
-
-	UnarySnowballStateTest(t, sbClone, 4, []int{1}, false)
-
-	binarySnowball := sbClone.Extend(0)
-
-	expected := "SB(Preference = 0, PreferenceStrength[0] = 4, PreferenceStrength[1] = 0, SF(Confidence = [1], Finalized = false, SL(Preference = 0)))"
-	require.Equal(expected, binarySnowball.String())
-
-	binarySnowball.RecordUnsuccessfulPoll()
-	for i := 0; i < 5; i++ {
-		require.Zero(binarySnowball.Preference())
-		require.False(binarySnowball.Finalized())
-		binarySnowball.RecordPoll(alphaConfidence, 1)
-		binarySnowball.RecordUnsuccessfulPoll()
-	}
-
-	require.Equal(1, binarySnowball.Preference())
-	require.False(binarySnowball.Finalized())
-
-	binarySnowball.RecordPoll(alphaConfidence, 1)
-	require.Equal(1, binarySnowball.Preference())
-	require.False(binarySnowball.Finalized())
-
-	binarySnowball.RecordPoll(alphaConfidence, 1)
-	require.Equal(1, binarySnowball.Preference())
-	require.True(binarySnowball.Finalized())
-
-	expected = "SB(PreferenceStrength = 4, SF(Confidence = [1], Finalized = false))"
-	require.Equal(expected, sb.String())
-}
diff --git a/snow/consensus/snowman/consensus_test.go b/snow/consensus/snowman/consensus_test.go
index bbeda976698b..cf1460605520 100644
--- a/snow/consensus/snowman/consensus_test.go
+++ b/snow/consensus/snowman/consensus_test.go
@@ -691,7 +691,7 @@ func RecordPollTransitivelyResetConfidenceTest(t *testing.T, factory Factory) {
 	votesFor3 := bag.Of(block3.ID())
 	require.NoError(sm.RecordPoll(context.Background(), votesFor3))
 	require.Equal(2, sm.NumProcessing())
-	require.Equal(block2.ID(), sm.Preference())
+	require.Equal(block3.ID(), sm.Preference())
 
 	require.NoError(sm.RecordPoll(context.Background(), votesFor3))
 	require.Zero(sm.NumProcessing())
@@ -1301,6 +1301,10 @@ func ErrorOnTransitiveRejectionTest(t *testing.T, factory Factory) {
 	require.ErrorIs(err, errTest)
 }
 
+func TestRandomized(t *testing.T) {
+	RandomizedConsistencyTest(t, TopologicalFactory{factory: snowball.SnowflakeFactory})
+}
+
 func RandomizedConsistencyTest(t *testing.T, factory Factory) {
 	require := require.New(t)
 
diff --git a/snow/consensus/snowman/mixed_test.go b/snow/consensus/snowman/mixed_test.go
new file mode 100644
index 000000000000..a5b30d19dad9
--- /dev/null
+++ b/snow/consensus/snowman/mixed_test.go
@@ -0,0 +1,55 @@
+// Copyright (C) 2019-2024, Ava Labs, Inc. All rights reserved.
+// See the file LICENSE for licensing terms.
+
+package snowman
+
+import (
+	"fmt"
+	"testing"
+
+	"github.com/stretchr/testify/require"
+	"gonum.org/v1/gonum/mathext/prng"
+
+	"github.com/ava-labs/avalanchego/snow/consensus/snowball"
+)
+
+func TestConvergenceSnowFlakeSnowBall(t *testing.T) {
+	require := require.New(t)
+
+	params := snowball.Parameters{
+		K:                     20,
+		AlphaPreference:       11,
+		AlphaConfidence:       11,
+		Beta:                  20,
+		ConcurrentRepolls:     1,
+		OptimalProcessing:     1,
+		MaxOutstandingItems:   1,
+		MaxItemProcessingTime: 1,
+	}
+
+	for peerCount := 20; peerCount < 2000; peerCount *= 10 {
+		numNodes := peerCount
+
+		t.Run(fmt.Sprintf("%d nodes", numNodes), func(t *testing.T) {
+			n := NewNetwork(params, 10, prng.NewMT19937())
+			for i := 0; i < numNodes; i++ {
+				var sm Consensus
+				if i%2 == 0 {
+					factory := TopologicalFactory{factory: snowball.SnowflakeFactory}
+					sm = factory.New()
+				} else {
+					factory := TopologicalFactory{factory: snowball.SnowballFactory}
+					sm = factory.New()
+				}
+
+				require.NoError(n.AddNode(t, sm))
+			}
+
+			for !n.Finalized() {
+				require.NoError(n.Round())
+			}
+
+			require.True(n.Agreement())
+		})
+	}
+}
diff --git a/snow/consensus/snowman/network_test.go b/snow/consensus/snowman/network_test.go
index 5e89280a2989..dc6781806e6a 100644
--- a/snow/consensus/snowman/network_test.go
+++ b/snow/consensus/snowman/network_test.go
@@ -51,6 +51,7 @@ func NewNetwork(params snowball.Parameters, numColors int, rngSource sampler.Sou
 			HeightV: dependency.HeightV + 1,
 		})
 	}
+
 	return n
 }
 
@@ -63,6 +64,7 @@ func (n *Network) shuffleColors() {
 		colors = append(colors, n.colors[int(index)])
 	}
 	n.colors = colors
+
 	utils.Sort(n.colors)
 }
 
@@ -74,12 +76,14 @@ func (n *Network) AddNode(t testing.TB, sm Consensus) error {
 	}
 
 	n.shuffleColors()
+
 	for _, blk := range n.colors {
 		copiedBlk := *blk
 		if err := sm.Add(&copiedBlk); err != nil {
 			return err
 		}
 	}
+
 	n.nodes = append(n.nodes, sm)
 	n.running = append(n.running, sm)
 	return nil
diff --git a/snow/consensus/snowman/snowman_block.go b/snow/consensus/snowman/snowman_block.go
index 236c93645a02..84b14422287e 100644
--- a/snow/consensus/snowman/snowman_block.go
+++ b/snow/consensus/snowman/snowman_block.go
@@ -36,7 +36,7 @@ func (n *snowmanBlock) AddChild(child Block) {
 	// if the snowball instance is nil, this is the first child. So the instance
 	// should be initialized.
 	if n.sb == nil {
-		n.sb = snowball.NewTree(snowball.SnowballFactory, n.t.params, childID)
+		n.sb = snowball.NewTree(n.t.Factory, n.t.params, childID)
 		n.children = make(map[ids.ID]Block)
 	} else {
 		n.sb.Add(childID)
diff --git a/snow/consensus/snowman/topological.go b/snow/consensus/snowman/topological.go
index 9888652f0764..c3939297fb4c 100644
--- a/snow/consensus/snowman/topological.go
+++ b/snow/consensus/snowman/topological.go
@@ -29,16 +29,20 @@ var (
 )
 
 // TopologicalFactory implements Factory by returning a topological struct
-type TopologicalFactory struct{}
+type TopologicalFactory struct {
+	factory snowball.Factory
+}
 
-func (TopologicalFactory) New() Consensus {
-	return &Topological{}
+func (tf TopologicalFactory) New() Consensus {
+	return &Topological{Factory: tf.factory}
 }
 
 // Topological implements the Snowman interface by using a tree tracking the
 // strongly preferred branch. This tree structure amortizes network polls to
 // vote on more than just the next block.
 type Topological struct {
+	Factory snowball.Factory
+
 	metrics *metrics
 
 	// pollNumber is the number of times RecordPolls has been called
diff --git a/snow/consensus/snowman/topological_test.go b/snow/consensus/snowman/topological_test.go
index 540b5a8f2eb1..f85ed36b7261 100644
--- a/snow/consensus/snowman/topological_test.go
+++ b/snow/consensus/snowman/topological_test.go
@@ -3,8 +3,12 @@
 
 package snowman
 
-import "testing"
+import (
+	"testing"
+
+	"github.com/ava-labs/avalanchego/snow/consensus/snowball"
+)
 
 func TestTopological(t *testing.T) {
-	runConsensusTests(t, TopologicalFactory{})
+	runConsensusTests(t, TopologicalFactory{factory: snowball.SnowflakeFactory})
 }
diff --git a/snow/engine/snowman/config_test.go b/snow/engine/snowman/config_test.go
index fe13d4f474c1..c1649121ee44 100644
--- a/snow/engine/snowman/config_test.go
+++ b/snow/engine/snowman/config_test.go
@@ -34,6 +34,6 @@ func DefaultConfig(t testing.TB) Config {
 			MaxOutstandingItems:   1,
 			MaxItemProcessingTime: 1,
 		},
-		Consensus: &snowman.Topological{},
+		Consensus: &snowman.Topological{Factory: snowball.SnowflakeFactory},
 	}
 }
diff --git a/snow/engine/snowman/engine_test.go b/snow/engine/snowman/engine_test.go
index c7fa4f45bbe9..0e405754268e 100644
--- a/snow/engine/snowman/engine_test.go
+++ b/snow/engine/snowman/engine_test.go
@@ -3012,7 +3012,7 @@ func TestGetProcessingAncestor(t *testing.T) {
 				ctx = snowtest.ConsensusContext(
 					snowtest.Context(t, snowtest.PChainID),
 				)
-				consensus = &snowman.Topological{}
+				consensus = &snowman.Topological{Factory: snowball.SnowflakeFactory}
 			)
 			require.NoError(consensus.Initialize(
 				ctx,
@@ -3086,7 +3086,7 @@ func TestShouldIssueBlock(t *testing.T) {
 
 	require.NoError(t, blocks[0].Accept(context.Background()))
 
-	c := &snowman.Topological{}
+	c := &snowman.Topological{Factory: snowball.SnowflakeFactory}
 	require.NoError(t, c.Initialize(
 		ctx,
 		snowball.DefaultParameters,
diff --git a/vms/platformvm/vm_test.go b/vms/platformvm/vm_test.go
index ab31ba76402e..30dd57660d39 100644
--- a/vms/platformvm/vm_test.go
+++ b/vms/platformvm/vm_test.go
@@ -1373,7 +1373,7 @@ func TestBootstrapPartiallyAccepted(t *testing.T) {
 			MaxOutstandingItems:   1,
 			MaxItemProcessingTime: 1,
 		},
-		Consensus: &smcon.Topological{},
+		Consensus: &smcon.Topological{Factory: snowball.SnowflakeFactory},
 	}
 	engine, err := smeng.New(engineConfig)
 	require.NoError(err)