| Monotonicity Criterion |
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The monotonicity criterion is a Voting System Criterion used to analyze both single and multiple winner Voting System s. A voting system is '''monotonic''' if it satisfies one of the definitions of the monotonicity criterion, given below. Douglas Woodall, calling the criterion mono-raise, defines it as: A candidate Mike Ossipoff defines the monotonicity criterion as: If an alternative X loses, and the ballots are changed only by placing X in lower positions, without changing the relative position of other candidates, then X must still lose. Both definitions are Logically Equivalent . This criterion may be intuitively justified by reasoning that in any fair voting system, no vote for a candidate, or increase in the candidate's ranking, should instead hurt the candidate. It is an important property considered in Arrow's Impossibility Theorem . It is generally considered a good thing if a voting system is monotonic. Clearly, non-monotonicity is very Counter-intuitive , although some do promote such systems (see Instant-runoff Voting ). Furthermore, although all voting systems are vulnerable to Tactical Voting , systems which fail the monotonicity criterion suffer an unusual form, where voters might try to elect their candidate by voting against that candidate. Tactical voting in this way presents an obvious risk if a voter's information about other ballots is wrong, however, and because of this non-monotonic voting systems may be somewhat discouraging of tactical voting. Of the single-winner voting systems, First Past The Post , Majority Choice Approval , Borda Count , Schulze Method , and Maximize Affirmed Majorities are monotonic, while Coombs' Method and Instant-runoff Voting are not. The single-winner methods of Range Voting and Approval Voting are also monotonic as one can never help a candidate by reducing or removing support for them, but these require a slightly different definition of monotonicity as they are not Preferential systems. Of the multiple-winner voting systems, all Plurality Voting methods are monotonic, such as Bloc Voting , Cumulative Voting , and the Single Non-transferable Vote . Those versions of the Single Transferable Vote which simplify to Instant Runoff when there is only one winner are not monotonic. EXAMPLE Suppose a President were being elected by Instant Runoff . Also suppose there are 3 candidates, and 100 votes cast. The number of votes required to win is therefore 51. Suppose the votes are cast as follows: |
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