[EM] Majority Criterion poor standard for elections

[Abd ul-Rahman Lomax]

On the Range Voting list, there has been an interesting discussion of 
the philosophy behind Range Voting vs preference-based methods (such 
as those satisfying the Condorcet Criterion and the Majority Criterion).

 From Wikipedia:

>The majority criterion is a 
><http://en.wikipedia.org/wiki/Voting_system_criterion>voting system 
>criterion, used to objectively compare 
><http://en.wikipedia.org/wiki/Voting_system>voting systems. The 
>criterion states that if a majority of voters strictly prefers a 
>given candidate to every other candidate (i.e. the given candidate 
>is the first preference of more than half the voters) and they vote 
>sincerely, then that candidate should win.

I should really touch that article, for the term "objectively," while 
technically correct, implies something that is not true: that systems 
which satisfy the majority criterion are superior to those which do not.

The problem with the majority criterion is that it entirely neglects 
strength of preference. Warren Smith, in his writing about Range 
Voting, has pointed this out: for some voters, the choice may be a 
matter of life and death, and for others, it may be a mere 
preference, or even no preference at all, the voter tossed a coin....

If a group of people for some reason can only order one kind of 
pizza, how can they choose which kind? Range Voting, where each 
person votes a numerical value for each choice, Warren prefers 
systems that are 0-99, but technically Range includes systems all the 
way from Approval Voting (value integers from zero to one) to even 
more refined systems, such as one where, in comparing items, the 
voter may assign any number and then the scores are normalized so 
that the highest vote given reduces to the maximum in whatever system 
is used to compile the votes.

For some people, whether or not they choose pepperoni may be only a 
matter of whim, they like some of the other choices just as well, 
though maybe that particular day they have a preference. For others 
it may be very, very important: pepperoni may make them ill or may be 
religiously prohibited. If you care about the group welfare, Range 
Voting essentially maximizes group satisfaction.

The Majority Criterion, I could show, also causes the voting system 
to devalue, effectively, the votes of knowledgeable voters, making 
them equal to those of those who are not knowledgeable. While we 
often think of strong opinions as representing fanaticism, the fact 
is that those who are knowledgeable about a subject are likely to 
have much stronger opinions about it -- so strong that their opinions 
may even be admitted as evidence, "expert opinion," -- than those who 
are not informed. When the uninformed have strong opinions, we would 
hope that these opinions could be given less weight, but I see no way 
to do this without violating the  basic criteria of democracy; 
however, a rational system would at least allow voters to indicate 
how strong their preferences are.

And if the voting system takes into account strength of preference, 
it does not satisfy the majority criterion.

A proposal has been made that if a Range poll shows a different 
winner, by summation of votes, than would be indicated through 
preference analysis -- which is easy to do with Range votes -- then 
there would be a ratification poll. Thus the Range winner would never 
be imposed on a majority, and the overall system would, indeed, 
satisfy the intention behind the Majority Criterion.

The Condorcet winner could, quite easily, not be the winner who would 
maximize social satisfaction with the result....