[EM] What is the ideal election method for sincere voters?

Abd ul-Rahman Lomax abd at lomaxdesign.com
Wed Mar 7 22:56:16 PST 2007

At 08:03 PM 3/7/2007, Scott Ritchie wrote:
>On Wed, 2007-03-07 at 13:41 -0500, Abd ul-Rahman Lomax wrote:
> > If we consider the underlying preferences and ratings to be
> > expressable in Range, then we can consider that the sincere voter
> > sets -- or can be seen as setting -- an Approval cutoff rating, and
> > all candidates rated above that level are approved and all below it
> > are not. Essentially, the voter has divided the candidates into two
> > sets, and the vote is sincere if every candidate in the approved set
> > is preferred to every candidate in the disapproved set.
> >
> > There is no known good reason for voting insincerely under Approval.
> > It is never forced.
>This definition bothers me a bit.

I can sympathize.

>   We tend to think of "sincere" votes
>as non-strategic, but the method you just described for "voting
>sincerely" can involve a whole lot of strategy based around resizing the
>sets and setting the approval threshold.

If the underlying ratings are accurate, in my view, a sincere voter 
does not become insincere through the setting of an approval cutoff 
at any level. While this could be called "strategic," and it 
certainly would change with knowledge of the general condition of 
society, it could only be "insincere" in a technical sense that 
assumes insincerity if a vote is altered based on what the voter 
thinks might fly.

Placing the Approval cutoff is a *judgement* that the voter makes. 
The *sincere* judgement would be based on "Given what I know about 
possibilities, what am I willing to accept."

If we ask the raw question of the voter, if wishes could be horses, 
what would you accept or "approve," a voter might simply select the 
favorite and any candidate absolutely equal to this. But that is not 
what we are seeking. We are seeking, in Approval, for the voter to 
set a "compromise" cutoff.

It is as if there were two elections: in one voters sincerely rate 
candidates. There still is a similar problem, but the essence of 
sincere rating is that the numbers reflect the preference strengths 
of the voter, not some judgement of what will succeed. If you think 
that Joe will make a fabulous President, the best possible, in 
sincere ratings you would have Joe at the top. If you think that 
someone else would be excellent, but not as good as Joe, then you 
would rate this other person highly, but lower than Joe. You would 
not take into consideration that lowering that rating could cause the 
second person to lose to a less desired candidate. Rather, you would 
simply rate candidates according to your estimation of their value in 
the office. If you prefer one candidate to another, but the 
preference is very slight, less than the resolution of the Range 
election, you might rate them identically, it would not be insincere.

Then there is the second election: what is the Approval cutoff? In 
this election I must consider what I think attainable. The fact is 
that I'd make a better choice in this regard if I have the results of 
the Range election first. Setting the Approval cutoff is a more 
difficult decision to make "accurately" than rating the candidates, I 
expect. But most voters simply won't make it that complicated. As 
I've frequently mentioned, I'd expect, unless the candidate field 
broadens significantly over present practice, most voters will simply 
vote for their favorite, which will be one of two frontrunners. A few 
voters will have a favorite who is not a frontrunner, and these will, 
as suggested, vote for their favorite and the frontrunner they 
prefer. And maybe for more than that, depends.

But if there are more than two frontrunners, more than two in reach 
of winning the election, it could get quite complicated....

So, the good news is that coming up with a set of sincere ratings 
should not be terribly difficult (as long as we don't insist that 
they be nailed down precisely). I'd probably start with a ranking, 
because pairwise comparison is easier. I doubt that I'd get caught in 
a Condorcet cycle!

Then I would set my least favorite at zero and my favorite at max and 
then work in between. Theoretically, I don't have to use the 
extremes, but if I consider that my vote should count equally with 
others, I would.

But to vote Approval requires an additional, substantially more 
complicated step if I want to do it precisely with a large number of 
candidates. I must set the approval cutoff. This is not dependent 
solely upon candidate preferences and ratings. Rather, it is 
dependent upon what compromises I'm willing to accept. If I approve a 
candidate who I'm actually not willing to accept, I'd leave the 
country if he wins, I'd call that insincere. And if I disapprove of a 
candidate whom I'd actually be pleased to have win, I'd similarly 
call that insincere. But there is a lot of room between these two rocks.

I don't see any forced insincerity in Approval. It might look like 
that because of confusion between the two separate decisions.

One test would be, if A is presented for ratification of his 
election, would I vote for or against A? I'd call a "fully" sincere 
Approval vote a vote on this question. And, in fact, Approval has 
been described that way.

But that is fairly demanding of compromise, because the pain of the 
election failing might be worse than the pain of an even fairly bad 
winner. This is equivalent to having NOTA on the ballot, and 
approving of any candidate one would prefer to NOTA. Libertarians 
might have a very simple ballot to fill out!

>We're not doing that though.  We're both acting very strategically here
>based on information about other voters to influence the election
>outcome, and at least one of us is changing our vote as a result.  That
>fits just about any reasonable definition of "strategic voting" yet
>you're calling us both sincere.

Some reserve "strategic voting" for voting where one reverses 
preferences to gain strategic effect. We could call that "fully insincere."

Approval never requires full insincerity, nor does Range. I gave a 
definition above for full sincerity in Approval. Full sincerity in 
Range isn't so difficult.

In Range and Approval, full sincerity may be strategically 
suboptimal, that is, the voter may be able to improve expected 
outcome by, for example, not Approving of a candidate that the voter 
would actually accept.

In an election between Bush Sr. and Clinton, I would, in fact, accept 
either. But this does not mean that I would vote for Bush Sr. I 
didn't, and not just because voting for both would have invalidated my ballot.

The fact is that the real election was between the two. With two 
candidates, Approval cutoff is pretty easy to set! You just approve 
your favorite. Because if you really didn't care, you could 
accomplish the same "not care" effect by not voting at all.

Rather, remember, the goal of voting is to use aggregated preference 
to select the ideal winner. So if I have a preference, I should 
express it. Does this mean that the method should allow me to express 
all preferences?

Not necessarily. Election methods are an attempt to compress 
deliberative process into a single poll. Approval compresses the 
process in a certain way, as I've noted, it asks two questions, the 
answer to the first being concealed and not directly expressed, it is 
only input to the second question.

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