User:Matijaskala/Probabilistic Approval Voting: Difference between revisions

'''Probabilistic Approval Voting''' is a sequential [[Proportional representation|proportional voting system]] that uses either [[Approval ballot|approval]] or [[Score voting|score]] ballots. ItsProbabilistic winnerscalculations are foundused byas thea usetool to predict potential power balance of probabilisticelected calculationspolitical factions. The method itself is deterministic. The system is 2-level [[Summability criterion|precinct-summable]] and passes the [[universally liked candidate criterion]].

Let's say that there is a functioncandidate P:A C×Cproposes ->a [0,1]decision. which returns theThe probability that two given candidates belong to the same political faction. Then for a given candidate Asupports the expected number of elected candidates belonging to the same factiondecision equals <math display="inline">\sum_frac{XV(A \inand WB)} P{V(A,XB)}</math>. andExpected thenumber expectedof averagevotes loadthat ofthe A'sdecision votersgets equals <math display="inline">\frac{\sum_{XB \in W} P\frac{V(A,X \and B)}{V(AB)}</math>. If A is not already elected then we can calculate the expected average load of A's voters after A's election asor <math display="inline">\frac{1+\sum_{XB \in W} P\frac{V(A,X \and B)}{V(B)}}{V(A)}</math> per voter. Let'sTo callminimize number of votes per voter we maximize <math display="inline">\frac{V(A)}{1+\sum_{X \in W} P(A,X)}</math> A's score and <math display="inline">\frac{1+\sum_{XV(A \inand W}P(A,X)}{V(AX)}}</math> A's inverse score. If we keep electing candidates whose inverse score is at least as low as inverse hare quota then we can expect an outcome wherefor each winner'snewly voters'elected expected average load is below a certain limit aka a proportional outcomecandidate.