Tie: Difference between revisions
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A type of tie is a symmetrical pairwise or ranked tie. For example:
<pre>
1 A>B>C
1 B>C>A
1 C>A>B
</pre>
All three candidates are in a symmetrical situation, that is, one could swap their name labels and they would still be in the exact same situation as before: ranked 1st on 1 ballot, ranked 2nd on 1 ballot, and ranked 3rd on 1 ballot. These types of ties are interesting in the context of evaluating [[Condorcet cycle|Condorcet cycles]]. They also feature when discussing an [[Equally Weighted Vote]]; some voting methods which pass the "test of balance" can fail to produce an equally weighted vote when there are symmetrical ties; this includes many voting methods which pass the [[majority criterion]] in the two-candidate case; see [[Equally Weighted Vote#Notes]] for an example.
=== Probability ===
Some voting method criteria are/must be defined with respect to candidates having or not having positive probability rather than winning or not winning. For example, the [[plurality criterion]] can be defined either as "B must not win" or "A's probability of winning must be at least as good as B's" (see also [[w:Plurality criterion]]).
== Tiebreaker procedures ==
Usually each tied candidate has an equal probability of winning. This can lead to technical (but likely very rare) failures of various criteria, however, so some more complex procedures have been created to avoid that.
=== Random Voter Hierarchy ===
See [[Maximize Affirmed Majorities#Random Voter Hierarchy tiebreak procedure]].
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