[EM] ignoring "strength of opinion"

[Abd ul-Rahman Lomax]

At 02:01 PM 12/1/2005, James Gilmour wrote:
>What I had in mind was if I vote 1, 2, 3, 4 (1 = most preferred, the 
>one I want to see win) for candidates A, B, C, D,
>and you vote 100, 99, 2, 1 (1 = most preferred) for the same four 
>candidates, it would be fundamentally undemocratic if
>your vote counted for more in determining the result just because 
>you expressed your preferences more strongly that I
>did.

Why? Such a voting method leaves the decision of how strongly to 
express a preference to the voter.

Let's suppose this is Range voting (that was not stated, but it is 
somewhat implied by the issue raised). The votes would, in range, 
generally not be expressed in the way stated. Range is *not* a 
preference-ordered system, though one can derive presumed preferences 
from it. In a Range system, ideally the voter is expressing 
utilities. I think it could be shown that the ideal strategy for 
Range would be to vote the most-preferred candidate as the maximum 
rating, for lowering that rating below that would simply dilute the 
vote, as stated. In a Range system, votes of 1,2,3,4 would be quite 
weird. Generally, Range implementations I've seen have the highest 
numerical rating being the most preferred.

Ratings (Range votes) have been confused with preferences (used in 
Condorcet methods), not just in how they would be analyzed but in how 
they would be collected as well.

To make sense of your votes in Range, I'd have to invert them. So you 
vote 4,3,2,1 for A,B,C,D, indicating that you prefer A most of all. 
The other voter votes 1,2,99,100, indicating a preference for D. You 
complain that the other voter's votes weigh more heavily. Well, yes, 
they certainly do. Why in the world, it would be asked, if you 
preferred A, did you only vote 4 for A instead of 100? In Range100, a 
4 is not how one would indicate a candidate considered qualified, it 
would be a candidate just short of (pick your favorite political bugaboo).

As I've indicated, some Range advocates propose normalizing Range 
Votes, but it is possible that good ballot design would make that 
unnecessary; and an argument against this is that voters should be 
*permitted* to express weak preferences. And if your preferences 
*are* weak, why should they be given great weight?

Yes, some voters will exaggerate, they will indicate drastic 
differences when they really don't have that opinion. But Range 
produces, I think, the maximum utility for voters if they vote their 
sincere preferences. If they don't, they, quite likely, only injure 
their effect on the election outcome.

For example, if you would honestly rate Nader 100, Gore 70, Bush 30, 
but you exaggerate to Nader 100, Gore 0, Bush 0, then you have done 
the most you can do to elect Nader, but you have effectively 
abstained from the contest between Gore and Bush. You have tossed 
away your chance to affect the election outcome.

Range is a method where there is no incentive not to rate your 
preferred candidate with the maximum rating. You are then essentially 
casting one full vote for that candidate (A range vote is really 
vote/maximum possible vote). If you want to, you can vote 
strategically with the rest of the candidates, for example, one might 
vote Nader 100, Gore 100, Bush 0. This is essentially Approval voting 
(Approval is Range2).

I've proposed a variant on Approval, it is essentially a Condorcet 
method with only three ranks, called, perhaps, Preferred, Approved, Rejected.

In one implementation, the Preferred and Approved votes are counted 
identically, so the election method is simply Approval, but the voter 
has been allowed to express a preference, which could be used, for 
example, to determine campaign finance allocations (thus solving one 
potential problem of Approval). In a more complex implementation, but 
still far simpler than full ranked Condorcet, the Preferred and 
Approval votes would be counted identically in all pairwise elections 
other than the ones involving a Preferred and an Approved candidate, 
in which case Preferred votes would count as a vote for the Preferred 
candidate and against the merely Approved candidate.

This is really truncated Condorcet.

>I can understand that there might well be some difference in the 
>social utility assessments of our preferences against
>the outcome, but the issue here is democratic representation and 
>"one person, one vote" surely comes above all else.

Your example was pretty confused, and it made it look like one person 
had, say, 100 votes, while the other had 4 votes. But, in fact, both 
persons had one vote. One of them used the full vote, and the other 
*elected* not to do so, but only used .025 vote. That was the voter's choice.

There is a lot of misinterpretation of "one person, one vote" out there....

>Once you depart from that (no matter what your opinion of the other 
>electors!), you are on a very slippery slope indeed.

"One person, one vote" was a slogan coined in an environment where 
literally only one vote could be cast. I.e., not only not Approval, 
but also not IRV, Condorcet, none of that.

The standard one-vote, winner-take-all system actually deprives many 
voters (sometimes *most* voters) of *any* vote.

One of the demonstrations that Approval, for example, is only a 
one-person, one-vote system is that the only *real* vote is one which 
chooses a winner. In Approval, either one has voted for the winner, 
in which case one has cast one effective vote, or one has not, in 
case one has cast *no* effective vote. In no case will more than one 
vote be other than moot (for purposes of determining a winner, there 
are other uses for votes). As to any of these other votes, if the 
voter had not cast them, the election outcome would not change.

But this brings up a point: in general, if a voter has not voted for 
a winner, the election outcome would not have changed had the voter 
not voted at all. Sometimes when I point this out, the objection is 
made that this is crazy, for there *must* be winners and losers.

Yes, an election will have winners and losers, but it is not at all 
difficult to design an election system, if we are talking about 
representation, where *every* vote actually counts, at least 
potentially, and quite possible nearly always. This is Asset voting, 
where the secret ballot assigns votes to "candidates" who are really 
electors. While this method can be used for single-winner elections, 
it is in multiwinner, proportional representation elections that 
Asset would function to maximum effect. A candidate who receives the 
quota is elected (or can choose a winner without restriction), and 
any excess votes can be assigned to a different candidate or candidates.