[EM] Range voting fails IIA

[Abd ul-Rahman Lomax]

At 08:59 PM 11/7/2006, 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."

Election criteria are supposed to be objective. One of the aspect of 
this, and I think it is -- or should be -- standard in applying the 
criteria, is that the mental state of the voters is not relevant. 
What is relevant is what is expressed on the ballots. (It was a 
failure to consider this that resulted in the error of considering 
Approval to have failed the Majority Criterion.)

One can certainly claim that an election method does not allow voters 
to express something, such as more than two ranks, or preference 
strengths. But that's not relevant here.

What does it mean to "add" a new alternative? In methods that are 
purely ranked, we presumably assume that the new candidate fits 
somewhere into the ranking system, and then the votes would be 
changed accordingly, with no other complications. We would assume 
that all relative ranks remain the same, for the candidates already 
in the election, and that the newcomer is simply assigned one of 
these ranks. If ranks must be exclusive, it is reasonable to allow 
that a new rank is inserted at some position for the candidate, but, 
again, except for that additional rank, nothing else changes.

The Range equivalent could only mean that the new alternative does 
not disturb the existing range ratings. And if this is the meaning, 
Range satisfies IIA, quite clearly.

What Mr. Cary did was to assume that the voters were following a 
strategy where one considers and adjusts Range votes based on the 
"candidate space." I.e., with this strategy, one ranks the best at 
max and the worst at zero, and then assigns values in between for the 
others, based on expectation of value.

However, this is internal process, and there are other reasonable 
strategies for the voter to follow. Moving toward Approval style 
voting is one of them. Approval satisfies IIA. Only if we think that 
the voter is following some strategy which causes the voter to change 
the approval votes already cast based on this newcomer could we say 
that it does not satisfy it.

But this is a ridiculous interpretation of IIA. Or at least it is one 
that becomes very hard to satisfy. I do not find IIA to be crisply 
defined. It seems to me that it is a criterion designed for ranked 
methods, because one may make ready assumptions about the effect of 
an added candidate on voting, by making presumptions about the effect of rank.

The nomination of Genghis Khan would probably not cause me to adjust 
my Range Votes for any candidate.... I'd simply rank him at zero. The 
nomination of a candidate that was obviously better to me than anyone 
else on the list, however, might indeed cause me to change my range 
ratings, and such adjustments might indeed, if other voters did not 
agree with me, cause a slippage for one of these such that he loses 
and the newcomer also loses. But this is hardly an "irrelevant 
alternative." I'd think of an irrelevant alternative as someone 
outside the reasonable candidate space, or, alternatively, a clone of 
a candidate already in that space. These would not ordinarily affect 
the winner, except possibly to substitute the newcomer for the 
previous winner, thus satisfying IIA.