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If voters are arranged on a sole 1-dimensional axis, such as the left-right political spectrum for a common example, and always prefer candidates who are more similar to themselves, a majority-rule winner always exists and is the candidate whose ideology is most representative of the electorate, a result known as the median voter theorem. [7]
Condorcet winner [Tn 1] Condorcet loser Smith [Tn 1] Smith-IIA [Tn 1] IIA/LIIA [Tn 1] Cloneproof Monotone Participation Later-no-harm [Tn 1] Later-no-help [Tn 1] No favorite betrayal [Tn 1] Ballot type First-past-the-post voting: Yes No No No No No No No No Yes Yes Yes Yes No Single mark Anti-plurality: No Yes No No No No No No No Yes Yes ...
Approval voting trivially satisfies the majority criterion: if a majority of voters approve of A, but a majority do not approve of any other candidate, then A will have an average approval above 50%, while all other candidates will have an average approval below 50%, and A will be elected.
An electoral system (or voting system) is a set of rules that determine how elections and referendums are conducted and how their results are determined.. Some electoral systems elect a single winner (single candidate or option), while others elect multiple winners, such as members of parliament or boards of directors.
The majority favorite criterion is a voting system criterion that says that, if a candidate would win more than half the vote in a first-preference plurality election, that candidate should win. Equivalently, if only one candidate is ranked first by a over 50% of voters, that candidate must win.
Dodgson's method is an electoral system based on a proposal by mathematician Charles Dodgson, better known as Lewis Carroll.The method searches for a majority-preferred winner; if no such winner is found, the method proceeds by finding the candidate who could be transformed into a Condorcet winner with the smallest number of ballot edits possible, where a ballot edit switches two neighboring ...
Most of the mathematical criteria by which voting systems are compared were formulated for voters with ordinal preferences. In this case, approval voting requires voters to make an additional decision of where to put their approval cutoff (see examples above). Depending on how this decision is made, approval satisfies different sets of criteria.
When mentioned without A voting system is winner-consistent if and only if it is a point-summing method; in other words, it must be a positional voting system or score voting (including approval voting). [3] [2]