[EM] Majority Criterion poor standard for elections

[Abd ul-Rahman Lomax]

At 11:30 PM 10/24/2006, Dave Ketchum wrote:
>What is this all about?

It's about the Majority Criterion and how neglecting strength of 
preference can, quite obviously, produce seriously suboptimal results 
in elections. Pure ranked ballots, which, with the exception of Range 
Voting, is most of what has been discussed on this list, thus are 
*inherently* defective.

>Let's forget "majority winner" for the moment, and look at the basic problem.
>
>Assume the voters are stubbornly split 3 ways such that for IRV or
>Condorcet they vote:

When you have a situation where the voters are "stubbornly split" 
like this, if it actually happens, you have a society which is about 
to implode. This society seriously needs a unifying candidate. In the 
election proposed, it is quite likely that "None of the Above" should win....

>     32 A
>     33 B
>     35 C
>     Condorcet will declare C the winner, without worrying about majority.
>     IRV will discard A and declare C majority winner of what is left.

The topic was the Majority Criterion. The Condorcet Criterion can 
indicate a winner who is essentially a plurality winner. The problem 
is the same.


>Range voters can give maximum possible range values to the above three
>candidates as best liked, plus minimum possible range values for any
>others they must include - thus agreeing that C is the proper winner.

Range voters may vote the extremes, bullet-vote, and if all do this, 
the election reduces to plurality. However, real elections are very 
unlikely to be like this. There will be candidates who are not rated 
at the extremes by some voters. If a field is so polarized that the 
votes would be as described, in the real world, other candidates will 
enter, attempting to gain votes across those boundaries. Unless the 
society itself is irretrievably polarized. In which case the country 
might need to be partitioned....

>Range voting is beyond me - couple thoughts:
>       Let voters be, at least mantally, identical twins - and the range
>values they assign could be consistent - but we DO NOT HAVE such voters.
>REAL voters have NON-identical minds.

Yes.

>       Voters CAN LEARN what values will have the strongest effect on
>assigning winners - and be tempted to use these values - perhaps due to
>greed; perhaps to respond to expected actions by other voters.

If a majority of voters vote out of greed, you will see a greedy 
result. With any election method.

The point made is that ranked ballots don't collect the information 
necessary to maximize social utility, only Range ballots do this. 
Some kind of hybrid method is proposed here, but I don't see any 
reason to use it over Range itself. Range can be a restricted set of 
values -- actually, Approval is a Range method reduced to binary. 
Trinary Range might be quite good, one way of ballot expression would 
be -1, 0, 1. This is quite equivalent to 0, 0.5, 1. The votes are 
summed and the winner is the candidate with the highest sum.

But the Range advocates generally want to see higher refinement of 
rating, the most common being 0 to 99. Personally, I think it is 
overkill. But maybe people would want that.

>Below I see mention of random.  Now true ties are possible, and random
>choices among them are fine,  But, for anything else, randomizing reads as
>losing interest in voters' preferences.

Or in the strength of their preferences.

What I'm suggesting is that the mere fact of preference tells us 
little about the value of the election of the preferred candidate 
over the election of another candidate, not preferred. They might be 
almost equal. Or they might be very much not equal.

I also made the point that knowledge can tend to increase strength of 
preference. Someone who knows all the candidates personally might be 
in a better position to make clear choices, compared to those who 
only have media impressions of them....