People can cast ballots {voting}| to determine election or referendum. Voting chooses among alternatives, perhaps allowing write-in candidates. Winner is choice with the most votes. Jurisdictions can require people to vote or restrict voting by literacy.
types
Voting can use different systems with different outcomes. From list, people can choose one alternative. If more than half the voters select one choice, it wins. If no choice has more than half the vote, choice with most votes can win, or runoff can select between the two choices with most votes. People can indicate preference order {proportional voting}. Vote counting weights preference order and selects most popular overall.
Simple majority rule can violate transitivity {Condorcet paradox, voting}, because rankings can permute in all ways {Condorcet cycle, voting}.
Democratic decisions can result if five assumptions hold {democratic voting}. With three or more candidates or proposed laws, the five assumptions are inconsistent.
Voters can prefer only one outcome {single-peaked preference}. With single-peaked preferences, voters choose outcome closest to preference, group preferences are transitive, and outcome is acceptable to all voters, because it is near middle.
If ballot has several alternatives, several voters will vote, voters have different preferences between any two alternatives, and outcome depends on more than one player, no method can find true group preference {social welfare function}. Preferences among some alternatives are independent of preferences for others, and if more people favor alternative, it stays favored {Arrow social welfare theorem}.
Voting rounds {sincere voting} can indicate people's true relative preferences.
Voting rounds {strategic voting} can invoke strategy to help people's true preference win.
Voters can indicate preference order. Count first eliminates lowest-ranked candidate and apportions that candidate's votes to remaining candidates. Count then eliminates lowest-ranked candidate and apportions that candidate's votes to remaining candidates, and so on, until only one candidate remains {instant-runoff voting} (IRV).
Candidate or proposition can win with the most votes {plurality voting}, even with no majority. Allowing plurality voting tends to merge parties, and voters tend to avoid extremes, so outcomes tend toward middle.
Number of representatives for a group can depend on group vote percentage {proportional representation}. This method allows more extremes, such as fringe parties. Under proportional representation, small groups that vote together usually have more power than large disorganized groups.
In one voting round, people assign rank, from 1 to candidate number, to all candidates {rank-order voting} {Borda count}. Winner has the most points. Because it is numerical, it can violate the neutrality principle.
Voting methods can first decide between two choices {successive procedure}, then decide between winner and third choice, then decide between winner and fourth choice, and so on. Final winner wins.
In one voting round, people list preference order among candidates {true majority rule} {simple majority rule}. Winner has won all one-on-one contests.
Voters have equal weight {equal treatment principle} {one-person one-vote principle} {anonymity principle}.
Election system gives no advantage to any candidate {symmetry principle} {neutrality principle}. Third-candidate presence or absence can have no affect on choice between two candidates. Third-candidate preference change can have no affect on outcome.
With several candidates, someone who always ranks below another person must not defeat that person {Pareto principle}.
If voter prefers candidate over second one, whom he or she prefers over third one, voter prefers first one over third one {transitivity principle}. In simple majority rule, if there are three candidates, and one is never second {value restriction}, transitivity holds. In simple majority rule, transitivity holds if all voters base decision on one parameter. Simple majority rule can violate transitivity {Condorcet paradox, transitivity} because rankings can permute in all ways {Condorcet cycle, transitivity}. In case of no simple majority, using rank-order to supplement vote maintains transitivity.
Outline of Knowledge Database Home Page
Description of Outline of Knowledge Database
Date Modified: 2022.0225