[Election-Methods] RE : Re: RE : Re: RE : Re: Simple two candidate election

[Abd ul-Rahman Lomax]

At 09:47 AM 12/25/2007, Kevin Venzke wrote:

> > [...] Range, voted with full strategic
> > effect, reduces to Approval Voting, which may reduce to bullet
> > voting. It *still* is not Plurality, because it only takes a few
> > percent of voters adding multiple votes to eliminate the spoiler effect.
>
>So you say that if Range is not quite as bad as Plurality, then that's "as
>well as hoped" for Range? I think most Range advocates have higher hopes.

No. But I can understand why Mr. Venzke would think that's my 
position. When a writer writes something that, without careful 
reading, can be interpreted to confirm some stereotype, it's very 
easy to overlook contradictory details. Further, an extension of the 
Wikipedia principle of Assume Good Faith, which is to assume that a 
writer is actually saying something of interest, would require not 
being satisfied with a shallow and meaningless interpretation.

Read what I wrote. I described what happens under certain conditions, 
the *worst* case. And then I noted that a few voters voting other 
than Plurality style are enough to solve the number one problem with 
Plurality. That's not shabby, particularly for Approval, which 
accomplishes this at no cost, merely starting to do what should have 
been a no-brainer from the beginning. It's the elephant in the living 
room, we never noticed, thought he was part of the furniture.

I did a study of strategic voting in Range 3, using some simple 
assumptions: three candidates, many voters, utilities for the voter 
of 1.0, 0.5, 0, and zero knowledge. Turns out that the sincere vote 
utility is equal to the "strategic vote" utility in that case, which 
is the same whether the voter votes (1,0,0), or (1,1,0). The claim 
that bullet voting is higher utility is not correct, it depends. 
*Accurate* sincere voting is on a par, at least, with "strategic 
voting," but there were different implications. The exaggerated vote 
resulted, as one might predict, in more wins for the favorite. But it 
also resulted in more wins for the least-favored. The sincere vote 
was less variable in result.

There was another interesting result from that study: if we take the 
Range election, with equal expected outcome for both the sincere vote 
and the strategic vote, and make it an Approval election, i.e., 
restrict the set of legal votes to the Approval style votes, the 
expected outcome *declines.* The existence of even one voter who 
votes intermediate causes the entire vote distribution to dither, 
increasing accuracy, at least that's my theory of why this occurred.

(More study is needed to confirm this; Warren Smith did co-author a 
page on it at rangevoting.org, so I think the math is sound; but the 
implications of converting to pure Approval have not been confirmed.)

However, first things first. While Range may be theoretically 
superior, Approval does improve results quite a bit in the 
simulations, and it is blatantly obvious why. Approval is free, just 
Count All the Votes. In the ranked form, Bucklin, it was used fairly 
widely in the U.S. at one time, though before the living memory of 
nearly everyone.

Consider this an election, and electability is important. The 
candidates are Plurality, IRV, Approval, Range, Condorcet. How would 
we vote in this election, held right now, assuming some level of 
public education in the campaign? How should the election be held? 
What method should be used?

The Range Voting people are *all*, to my knowledge, supporting 
Approval at this time. While CRV is doing a level of educational 
effort regarding Range, it's Approval which is seeing real advocacy. 
It has a solid history of academic study. It's significant enough 
that FairVote is putting some considerable effort into finding ways 
to attack it. Simple, cheap, easy to understand, strategy very 
simple, no surprises, solves the spoiler problem, but has no center 
squeeze effect. Center squeeze is not important in a two-party 
system, but what if election reform lives up to the sometimes-implied 
promise that it helps third parties gain a toehold?

>Your claim that strategic Range voters are actually sincere is not
>different from choosing to believe that the Plurality winner is always the
>favorite candidate of the most voters.

I'm disappointed. Mr. Venzke, I've seen much better analysis from 
you. Look again.

In Range, there is no strategic advantage, ever, to reverse expressed 
preference from real preference. The so-called "insincere" vote in 
Range is simply a non-linear squeeze of the internal utilities, or 
another way to put it, the internal absolute utilities are 
normalized, first -- nearly everyone will do that, since an election 
is a choice, and choices are almost automatically normalized -- then 
the scale is expanded depending on two factors: expectations of how 
the electorate as a whole is likely to vote, and the effort the voter 
is willing to put into determining how to vote. Approval-style voting 
is relatively easy, and a lot of voters are going to do just that.

In Plurality, by contrast, strategic voting requires preference 
reversal, as with all ranked methods where equal ranking is not allowed.

It's simpler to see with Approval. I claim that a sincere vote in 
Approval is a vote which divides candidates into two sets: Approved 
and Not Approved. There is no reason for a voter to insincerely vote 
(other than through misunderstanding the implications, and they are 
pretty simple); an insincere vote would be voting for a candidate 
when another candidate preferred over him or her does not get a vote.

What most voters will do with Approval is to vote for their favorite, 
first. They will also vote, most of them, for their preferred 
frontrunner, since all other votes are likely to be moot. And then, 
if they understand the system, they will likewise vote for any other 
candidates they also prefer to the frontrunner they voted for. But 
those third votes will be rare, and, practically by definition, in a 
two-party system, most voters would vote for only one.

Range is obviously more complex to vote, but the basic principles are 
the same. I'd expect nearly all voters, once Range is understood, to 
vote the extremes for at least one candidate each. It's been argued 
that votes should be normalized, to correct for weak votes, on the 
theory that these were due to voter ignorance. Indeed, that was a 
proposal of mine. I later came to think it was a bad idea. Voters 
voting weak opinions *when they really do not have a strong 
preference and choose to partially abstain* actually improves outcome.

It's easy to see why. Under Plurality, voters who don't care which of 
the frontrunners wins current may choose not to vote, or just don't 
go to the trouble. There is lots of handwringing over this, but, in 
fact it improves outcome over introducing noise. In face-to-face 
meetings, people who don't care about the outcome of a vote, they 
could accept either result, often abstain. As they should.

>  Essentially Range comes with a
>suggestion on how to rate candidates, that isn't motivated by the method's
>incentives. And then no matter how people vote, you choose to interpret
>that they followed the suggestion.

What suggestion does Range "come with"? First of all, Center for 
Range Voting, mostly put together by a mathematician, is not an 
authority on ballot instructions.

Range voting is exactly equivalent to allowing fractional votes in an 
Approval election. Current ballot instructions say *nothing* about 
how to choose who to vote for. They do not say, "Vote for your 
Favorite," they certainly do not say, "Vote for your favored 
frontrunner." Approval ballots will not say, "Vote for all candidates 
you approve." If the ballots are as I would argue, they should merely 
describe what votes are legal and how the outcome will be determined, 
which is very, very simple with Range. Again, it is Just Count All 
the Votes. Candidate with the most votes wins.

I must say, though, that I don't understand Venzke's last comment, it 
refers to more than one unspecified abstraction: the "suggestion on 
how to rate candidates," the "method's incentives," and, further, 
some "choice to interpret." We add up the votes, we don't "interpret" 
them. (In my opinion, that's best; the 'official' CRV recommendation 
is still average vote, which introduces a whole can of wormy 
complications for no real benefit, and the simulations utterly 
neglect this as far as I know, it's just an opinion that got stuck in there.)

Approval instruction: Vote for all candidates you choose to support; 
the winner will be the candidate with the most votes.

Range instruction (Range 3, +/-): For each candidate, mark Yes or No 
or leave the boxes blank. The candidate with the highest result, 
after No votes are subtracted from Yes votes, will win. A blank vote 
will not affect the total. (This is Range 3, the three possible votes 
are -1, 0, +1; the default vote pulls the average toward the center. 
However, it is also possible that there would be an explicit zero, 
and that average result would be used. I don't care to debate this, 
at this time, there is plenty of time. If we can't get Approval, 
Range is really pie in the sky.)

Other possible instructions can be written for higher Range 
implementations and different treatment of abstentions; my own 
opinion probably that candidate abstentions should be treated as 
minimum rating, not mid rating, but this all really needs further study.

Range Voting, at least under that name, was invented by a 
mathematician, not a political scientist. The description of Range in 
terms of the *meaning* of the vote, aside from the real political 
meaning, is a red herring. Votes are actions, not sentiments. 
Sentiment is something that the voter uses and integrates with the 
voter's opinion of what is possible, sometimes, to decide how to act, 
but behind a single action may be quite different intentions.

To cover one more matter again: the application of the Majority 
Criterion to Approval depends on a quite problematic definition of 
"sincere vote," and James Armytage-Green struggles mightily with the 
problem on his page on this criterion. What he really ends up with, 
though he doesn't say it explicitly, is a definition of sincere vote 
in Approval as being not not sincere. Yes, double negative.

Is it insincere to say that the set of candidates A, B is preferred 
to the set of candidates, C, D, if the voter has a preference between 
A and B? Of course not. It is not full disclosure of preference, that 
is all. To make Approval fail the Majority Criterion -- there seems 
to be a strong intuition that it fails, and so a lot of effort into 
manipulating the definition so that it, indeed, fails, which makes 
mincemeat of the use of election criteria for objective judgement -- 
one must posit an internal preference that is not expressed, and, 
then, of course, if a preference is not expressed, it cannot be 
considered by the method and so the majority preference may fail to 
win. However, *any preference not expressed* can cause MC failure, 
and Plurality, as an example, is generally considered to pass MC. 
With Plurality, then, the criterion requires a "sincere vote." Which 
with plurality requires preference reversal, i.e., the voter prefers 
a candidate that the voter did not rank first.

However, with Approval, the voter may rank the favorite first, there 
is no motive not to do so. The question is about additional 
approvals. If the majority chooses not to express its preference 
*exclusively*, then, of course, it can fail to elect its favorite. 
How do we describe this vote? Is it sincere?

In the ordinary meaning, of course it is, there is no reason to 
presume otherwise. However, "sincere vote" is used technically in the 
Criterion. What does it mean?

The original Majority Criterion that I could find simply referred to 
the voter's "preference list." It did not address unexpressed 
preferences, it was written for ranked methods, and seems to have 
assumed that full ranking was allowed. If a majority strictly prefers 
one candidate over all others, that candidate must prevail. But 
unwritten was that the majority must express the preference. If a 
majority strictly prefers one candidate over all others, and 
expresses that preference, that candidate must prevail. Approval 
passes this criterion. Some have argued that defining the criterion 
this way makes it useless, but that's not true. Range does not pass 
the criterion, because "prefer" has no strength; a majority may have 
a weak preference which is overcome by a strong preference of a minority.

However, real world: It is certainly true that, with Approval, it 
could occur that the preference of a majority fails to be elected, if 
the majority adds votes which essentially cancel out the expression 
of this preference. But what has long been overlooked is that the 
situation in which this would happen would be extraordinarily rare 
under present conditions. We should be so luck as to see multiple 
majorities, which is what it takes! How often would voters vote for 
both frontrunners?

I'd say, let's work for Approval and see how it plays out. Then some 
experimentation with fractional votes. The cost of both of these is 
well under the cost of implementing ranked methods; Approval is 
essentially free. Did I mention that it as simple as:

Just Count All the Votes.