We assume discrete time and that no two users arrive simultaneously at the poll, i.e. one user arrives at time
At time
At time
At each time
- A new user
${u_t}$ votes for$0$ or$k \geq 1$ existing statements$v_t^1, \ldots ,v_t^k \in V_{t-1}$ . Voting creates the corresponding edges,${({u_t},v_t^1), \ldots ,({u_t},v_t^k)}$ , such that${E_{t - 1}} \cup \left{ {({u_t},v_t^1), \ldots ,({u_t},v_t^k)} \right} = {E_t}$ , or no edges in case of no voting (implying${E_{t - 1}} = {E_t}$ ). User${u_t}$ can also create$0$ or$l \ge 1$ new statements$v_t^1, \ldots ,v_t^l \notin {V_{t - 1}}$ , such that${V_{t - 1}} \cup \left{ {v_t^1, \ldots ,v_t^l} \right} = {V_t}$ (if no statements are created,${V_{t - 1}} = {V_t}$ ). - An existing, returning user
$u$ visited the poll latest at time$t^{'} < t$ , either as a new user or returning one (i.e. an existing user may return multiple times). On time$t$ they vote for$0$ or$k \geq 1$ existing statements$v_t^1, \ldots ,v_t^k \in V_{({t^{'}},t)}$ , where${V_{({t^{'}},{t-1})}}$ is the set of all statements added to the poll between time${t^{'}}$ and$t-1$ (possibly $\emptyset $ if${t^{'}} = t - 1$ ). Similarly to the previous case, user${u}$ can also create$0$ or$l \ge 1$ new statements$v_t^1, \ldots ,v_t^l \notin {V_{t - 1}}$ , such that${V_{t - 1}} \cup \left{ {v_t^1, \ldots ,v_t^l} \right} = {V_t}$ (if no statements are created,${V_{t - 1}} = {V_t}$ ).