[EM] Range voting fails IIA

[Chris Benham]

David Cary wrote:

>Both CRV and Wikipedia claim that range voting meets the Independence
>of Irrelevant Alternatives (IIA) criterion, but neither gives much
>justification for such claims.
>
>Electorama succinctly but informally describes IIA as:
>    "if one option (X) wins the election, and a new alternative (Y)
>is added, only X or Y will win the election."
>
>Wikipedia is nearly as informal but more restrictive in the scope of
>its application:
>    "If A is preferred to B out of the choice set {A,B}, then
>introducing a third, irrelevant, alternative X (thus expanding the
>choice set to {A,B,X} ) should not make B preferred to A. In other
>words, whether A or B is better should not be changed by the
>availability of X."
>
>But Range Voting doesn't satisfy IIA in either form.  Without loss of
>generality, we'll look at the range voting that allows ballots to be
>cast in the range from 0 to 100.  Then consider the following
>example:
>
>First, there are two candidates, A and B, and three voters, u, v, and
>w.  Each of the three voters have a personal scoring system for the
>candidates as follows:
>
>u: A= 450,  B= 270
>v: A=-320,  B=-200
>w: A= 590,  B= 730
>
>and the voters cast the following ballots:
>
>u: A=100, B=  0
>v: A=  0, B=100
>w: A=  0, B=100
>
>This produces totals of A=100, B=200, and B is the winner, beating A.
>
>Now a third candidate, C, is introduced.  The personal scoring system
>for each voter is extended to include C, but the scores for A and B
>are unchanged:
>
>u: A= 450, B= 270, C= 150
>v: A=-320, B=-200, C=-800
>w: A= 590, B= 730, C=  30
>
>and the candidates cast votes as:
>
>u:  A=100, B= 40, C=0     ( Vote = 1/3 * (Score - 150) )
>v:  A= 80, B=100, C=0     ( Vote = 1/6 * (Score + 800) )
>w:  A= 80, B=100, C=0     ( Vote = 1/7 * (Score -  30) )
>
>Which produces totals of A=260, B=240, C=0, and A is the winner,
>beating B and C. Hence a violation of IIA.
>
>Note that in each case all voters cast what some have described as
>sincere or honest votes.
>
>-- David Cary 
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>
The claim that Range meets IIA (and Clone Independence) rests on the 
assumption that the
voters' ratings are "absolute", based on some standard that is 
independent of  the candidates.

According to this assumption, Range doesn't reduce to FPP when there are 
two candidates.

Range promoters like to move the goal posts around. For example one who 
has claimed that
Range meets IIA also makes it clear that he expects that voters will 
always vote at least candidate
max. and at least one min.

Chris Benham



































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