[EM] RE : Re: RE : Majority Criterion, hidden contradictions

[Abd ul-Rahman Lomax]

At 01:30 AM 11/7/2006, Chris Benham wrote:

>Abd ul-Rahman Lomax wrote:
>90: A9>B1    (sincere is A9>B1)
>10: B99>A0  (sincere is B5>A3)
>
>All the voters have a sincere low opinion of both candidates, but 
>90% think that A is 900%
>better than B and yet B wins (with only 10% of the voters not being 
>"sincere and honest").

It is almost as if Chris said, there are 100 eligible voters. 90 of 
them stay home. 10 vote and the candidate they favor is elected.

Chris has assumed that a sincere Range vote would be an absolute 
number. Range votes are *relative* (just like other votes, 
generally). There is no intrinsic meaning to 99 or 0, beyond saying 
that 99 is "the best" and 0 is "the worst."

If voters do not choose a "best" and a "worst," i.e., vote 99 or 0 
for at least one candidate each, they have cast a weak vote. Casting 
a maximum vote of 9 out of a possible 99 is like casting one-tenth of a vote.

Range *allows* voters to cast weak votes. Ranked methods, including 
the simplest, plurality, don't allow weak votes. You either cast a 
full vote for a candidate (one only in the case of no-overvoting 
plurality) or no vote for that candidate. Ranked methods with more 
than two ranks break down into a series of pairwise elections, and, 
again, the vote in each pairwise election is either one vote for one 
side, or a vote for the other side, or an abstention.

Range allows intermediate votes. It does not require them. You can 
vote Range as Approval, if you like, and the effect of your vote is 
as it would be in approval.

The example given has 90% of the voters casting a weak vote. So of 
course they are outweighed by the 10% that cast votes at full strength.

More silliness from Chris.

>>
>That rests on the false assumption that it is (significantly) more 
>bother to lie than to tell the truth.
>In fact it seems to me to be less bother. I can well imagine being 
>sure that I prefer A to B but
>not sure exactly what my honest rating of each is, so I'd find it 
>easier to vote A max. and B min.

Fine. Chris has glossed over that the situation under consideration 
is that the voter prefers A to B, slightly, and both of them to C, 
substantially.

So if the voter wants less bother, the voter can vote A and B with 
high ratings, perhaps the max, and C at minimum. Or the voter, 
knowing that he prefers A to B, can vote A at max and B at min. *And C at min.*

This is a sincere vote. It is not a lie. Voters are not required to 
satisfy any definition of preference strength under Range. They may 
express what we might call a weak preference as strong, and they may, 
but are unlikely to do so, express a strong preference as weak (I see 
no reason why they would do this).

Lying, in the meaning I was using would be to reverse the actual 
preference. I.e., we are talking about strategic voting, *not* merely 
voting Approval style. The voter prefers B to C, but prefers A to be 
and fears that B will win unless the voter ranks B at minimum. The 
lie is not that the voter ranks B at minimum, but that the voter then 
ranks C higher than B even though the preference is the opposite.

I continue to be amazed at how Chris can generate these utterly 
spurious arguments.

>We can certainly be sure majoritarian methods will outperform  Range 
>in the worst-case scenarios.

Provocative statement made with utterly no evidence presented. 
Further, when you've got an election methods expert, "worst-case 
scenarios" can mean completely impossible vote arrangements, 
carefully constrained to create an outrageous result with this or 
that election method. I don't put this beyond Chris at all. Just look 
at the Range example he gave above. 90% of the voters deliberately 
cast a strange vote.

It is clear that Range, if not introduced gradually (which is what I 
personally recommend, i.e., starting with Approval), requires voter 
education. Even though the method is extremely simple, the 
consequences of not voting the full Range should be explicitly 
explained, so that voters don't remain unaware that this casts a weak 
vote. I would want all voters to know that they have the right to 
cast a full vote, and would want them to cast a weak vote only deliberately.

Because they are accustomed to standard full-vote/no-vote systems, 
this may not be immediately obvious to some of them. The vast 
majority of them would be able to figure it out (it is simplest to 
understand if Range is counted as the sum of votes), but it should 
still be explicitly explained.