Difference between revisions of "Strategy-free criterion"

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The '''strategy-free criterion''' is a [[voting system criterion]] for evaluating [[voting system]]s.
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== Definitions ==
 
== Definitions ==
   
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If one candidate is preferred over each of the other candidates, that candidate is called "Condorcet candidate" or "Condorcet winner".
 
If one candidate is preferred over each of the other candidates, that candidate is called "Condorcet candidate" or "Condorcet winner".
   
== Statement of Criterion ==
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== Statement of criterion ==
   
''If a Condorcet candidate exists, and if a majority prefers this candidate to another candidate, then the other candidate should not win if that majority votes sincerely and no other voter falsifies
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{{definition|If a Condorcet candidate exists, and if a majority prefers this candidate to another candidate, then the other candidate should not win if that majority votes sincerely and no other voter falsifies any preferences.}}
 
In a ranked method, it is nearly equivalent to say: {{definition|If more than half of the voters rank ''x'' above ''y'', and there is no candidate ''z'' whom more than half of the voters rank above ''x'', then ''y'' must not be elected.}}
any preferences.''
 
 
== Complying methods ==
 
In a ranked method, it is nearly equivalent to say: ''If more than half of the voters rank ''x'' above ''y'', and there is no candidate ''z'' whom more than half of the voters rank above ''x'', then ''y'' must not be elected.''
 
 
== Complying Methods ==
 
   
 
*'''Complies''': [[Schulze method]] (with winning votes as the measure of defeat strength), [[MDDA]], [[MAMPO]]
 
*'''Complies''': [[Schulze method]] (with winning votes as the measure of defeat strength), [[MDDA]], [[MAMPO]]
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The reader may be wondering how the Condorcet candidate, if one exists, could
 
The reader may be wondering how the Condorcet candidate, if one exists, could
possibly <em>not</em> be preferred by a majority of voters over any
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possibly ''not'' be preferred by a majority of voters over any
 
other candidate. The key is that some voters may have no preference
 
other candidate. The key is that some voters may have no preference
 
between a given pair of candidates. Out of 100 voters, for example, 45
 
between a given pair of candidates. Out of 100 voters, for example, 45
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In order to understand SFC, one must also understand that there are
 
In order to understand SFC, one must also understand that there are
 
two types of insincere votes: false preferences and truncated
 
two types of insincere votes: false preferences and truncated
preferences. Voters <em>truncate</em> by terminating their rank list
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preferences. Voters ''truncate'' by terminating their rank list
 
before their true preferences are fully specified (note that the last
 
before their true preferences are fully specified (note that the last
 
choice is always implied, so leaving it out is not considered
 
choice is always implied, so leaving it out is not considered
truncation). Voters <em>falsify</em> their preferences, on the other
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truncation). Voters ''falsify'' their preferences, on the other
 
hand, by reversing the order of their true preferences or by specifying
 
hand, by reversing the order of their true preferences or by specifying
 
a preference they don't really have. Suppose, for example, that a
 
a preference they don't really have. Suppose, for example, that a
voter's true preferences are (A,B,C,D). The vote (A) or (A,B) would be a
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voter's true preferences are (A,B,C) with no preference between D and E.
truncated vote, and the vote (B,A,C) or (A,C,B) would be a falsified
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The vote (A) or (A,B) would be a truncated vote, and the vote (B,A,C) or (A,C,B)
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or (A,B,C,D,E) would be a falsified vote.
vote.
 
   
 
SFC requires that the majority of voters who prefer the Condorcet candidate to
 
SFC requires that the majority of voters who prefer the Condorcet candidate to
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candidate to win by truncating their preferences. (In theory, that
 
candidate to win by truncating their preferences. (In theory, that
 
minority could cause the other candidate to win by falsifying their
 
minority could cause the other candidate to win by falsifying their
preferences, but that would be a very risky <em>offensive</em> strategy
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preferences, but that would be a very risky ''offensive'' strategy
 
that is more likely to backfire than to succeed.) The significance of
 
that is more likely to backfire than to succeed.) The significance of
 
the SFC guarantee is that the majority has no need for defensive
 
the SFC guarantee is that the majority has no need for defensive
 
strategy, hence the name Strategy-Free Criterion.
 
strategy, hence the name Strategy-Free Criterion.
   
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The [[Schulze method]] was shown to comply with both the Condorcet and Generalized Condorcet Criteria (CC and GCC) above. Although compliance with CC and GCC are important, those criteria apply only in the theoretically ideal case in which all votes are sincere. The Strategy-Free criterion goes further and shows that, under certain reasonable conditions, a majority of voters have no incentive to vote insincerely. The fact that the [[Schulze method]] also complies with SFC therefore enhances the significance of CC and GCC considerably.
[[Schulze method|Cloneproof Schwartz Sequential Dropping]] was shown to comply with both the
 
Condorcet and Generalized Condorcet Criteria (CC and GCC) above.
 
Although compliance with CC and GCC are important, those criteria apply
 
only in the theoretically ideal case in which all votes are sincere. The
 
Strategy-Free criterion goes further and shows that, under certain
 
reasonable conditions, a majority of voters have no incentive to vote
 
insincerely. The fact that [[Schulze method|Cloneproof Schwartz Sequential Dropping]] also complies with SFC
 
therefore enhances the significance of CC and GCC considerably.
 
   
 
''Some parts of this article are derived with permission from text at http://electionmethods.org''
 
''Some parts of this article are derived with permission from text at http://electionmethods.org''
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== See also ==
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*[[Voting system]]
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*[[Monotonicity criterion]]
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*[[Condorcet Criterion]]
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*[[Generalized Condorcet criterion]]
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*[[Generalized Strategy-Free criterion]]
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*[[Strong Defensive Strategy criterion]]
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*[[Weak Defensive Strategy criterion]]
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*[[Favorite Betrayal criterion]]
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*[[Participation criterion]]
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*[[Summability criterion]]
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== External links ==
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* [http://electionmethods.org/ electionmethods.org]
 
{{fromwikipedia}}
 
{{fromwikipedia}}
 
[[Category:Voting system criteria]]
 
[[Category:Voting system criteria]]

Latest revision as of 23:20, 19 October 2019

The strategy-free criterion is a voting system criterion for evaluating voting systems.

Definitions[edit | edit source]

A sincere vote is one with no falsified preferences or preferences left unspecified when the election method allows them to be specified (in addition to the preferences already specified).

One candidate is preferred over another candidate if, in a one-on-one competition, more voters prefer the first candidate than prefer the other candidate.

If one candidate is preferred over each of the other candidates, that candidate is called "Condorcet candidate" or "Condorcet winner".

Statement of criterion[edit | edit source]

If a Condorcet candidate exists, and if a majority prefers this candidate to another candidate, then the other candidate should not win if that majority votes sincerely and no other voter falsifies any preferences.
In a ranked method, it is nearly equivalent to say:
If more than half of the voters rank x above y, and there is no candidate z whom more than half of the voters rank above x, then y must not be elected.

Complying methods[edit | edit source]

Commentary[edit | edit source]

The reader may be wondering how the Condorcet candidate, if one exists, could possibly not be preferred by a majority of voters over any other candidate. The key is that some voters may have no preference between a given pair of candidates. Out of 100 voters, for example, 45 could prefer the Condorcet candidate over another particular candidate, and 40 could prefer the opposite, with the other 15 having no preference between the two. In that case, it is not true that a majority of voters prefer the Condorcet candidate over the other candidate, and SFC does not apply.

In order to understand SFC, one must also understand that there are two types of insincere votes: false preferences and truncated preferences. Voters truncate by terminating their rank list before their true preferences are fully specified (note that the last choice is always implied, so leaving it out is not considered truncation). Voters falsify their preferences, on the other hand, by reversing the order of their true preferences or by specifying a preference they don't really have. Suppose, for example, that a voter's true preferences are (A,B,C) with no preference between D and E. The vote (A) or (A,B) would be a truncated vote, and the vote (B,A,C) or (A,C,B) or (A,B,C,D,E) would be a falsified vote.

SFC requires that the majority of voters who prefer the Condorcet candidate to another particular candidate vote sincerely (neither falsify nor truncate their preferences), and it also requires that no other voter falsifies preferences. SFC therefore implies that the minority that does not prefer the Condorcet candidate to the other candidate cannot cause the other candidate to win by truncating their preferences. (In theory, that minority could cause the other candidate to win by falsifying their preferences, but that would be a very risky offensive strategy that is more likely to backfire than to succeed.) The significance of the SFC guarantee is that the majority has no need for defensive strategy, hence the name Strategy-Free Criterion.

The Schulze method was shown to comply with both the Condorcet and Generalized Condorcet Criteria (CC and GCC) above. Although compliance with CC and GCC are important, those criteria apply only in the theoretically ideal case in which all votes are sincere. The Strategy-Free criterion goes further and shows that, under certain reasonable conditions, a majority of voters have no incentive to vote insincerely. The fact that the Schulze method also complies with SFC therefore enhances the significance of CC and GCC considerably.

Some parts of this article are derived with permission from text at http://electionmethods.org

See also[edit | edit source]

External links[edit | edit source]

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