[Election-Methods] Response to Schudy re Range vs Approval voting

[Abd ul-Rahman Lomax]

I've been over and over this point, there is little in this post that 
is new. I'd suggest reading it carefully. And if you wish to continue 
asserting that Range can "cause a mess" when voters vote a mixture of 
"sincere" voting and Approval-style voting, please define "sincere" 
in a manner that we could agree upon, define what a sincere Range 
vote is, and how, and *how much* the voters are harmed by voting 
sincerely, and what effect this has on society as a whole.

Otherwise, the assertion is just blowing smoke and confusion.At 12:03 
AM 8/9/2007, Juho wrote:
>>It happens, however, that you can think about Range that way if you
>>want. It can be used to maximize social utility, and it does a
>>pretty good job even if most voters vote the extremes.
>
>Maximizing social utility refers to giving sincere utilities in the
>ballots.

No. Not necessarily. If you don't give some kind of "sincere" utility 
on the ballot, *your* utility won't be maximized!

However, the word "sincere" isn't precisely defined with Range. Lots 
of writers have assumed that there is some "sincere utility" that 
would automatically translate to a specific Range vote. Of course, 
Warren Smith, in designing his simulators, had to face the fact that 
there is no such thing.

We can easily define "insincere" with Range, and the definition 
covers ranked methods exactly, except for ranked methods which allow 
equal ranking. When equal ranking is allowed, ranked methods start to 
resemble Range in that small way....

"Insincere" refers to reversing a preference; that is, you prefer A 
over B but your ballot shows that you prefer B over A. Plurality, 
with no overvoting, for starters, requires "insincere voting" if you 
prefer a third party candidate who has no chance of winning, and want 
to influence the outcome of the real election.

Range methods never provide an incentive to reverse preference. Now, 
when I propose Range+PW, there comes to be a ranked aspect to the 
election, so it is possible that one could discover some such 
incentive, but the strategic considerations, it seems to me, become 
so twisted and unlikely that I doubt anyone would do it. Condorcet 
methods do provide some motive for insincere voting, but even there 
it is controversial how much people would actually do it. With 
Range+PW, I haven't examined the characteristics of the hybrid method 
in detail, but it seems to me quite a stretch that a solid strategic 
motive for reversal would be found. In Range+PW, the goal is to get 
your favorite in the runoff, or, failing that, your favorite from 
among the top few candidates.

I should note that Range and Approval, without special rules, are 
"Plurality" methods. Approval makes it more likely that a winner will 
have a "majority," but certainly does not guarantee it, and 
"strategic" considerations make an Approval majority less clear if 
there exists more than one candidate with it.

Some consider that Approval can elect a winner who would lose a 
pairwise election with another candidate to be a feature of Approval. 
It is, to a degree. My opinion is that whenever a majority surrenders 
its preference, it should do so knowingly. It's generally impossible 
to fully consider this in a single-stage election.

(It's possible, if the voters specifically consent to it, with the 
same ballot. It gets murky if, instead, they pass a law to apply to 
future elections. It's a *different* majority in that case!)

>  You seem to be recommending the voters to primarily do so,

I do recommend not reversing preferences. As to the expression of 
so-called sincere ratings -- what is that? -- I suggest 
normalization, for starters, in nearly all circumstances. In some, 
what I call the "first normalization" would remain proper, not the second.

(The first normalization: the voter considers *all* possible 
candidates, not just those on the ballot. The voter assigns 100% to 
the best of these and 0% to the worst. This is pretty much what 
Warren does with his simulations, to generate "sincere" and "not 
normalized" utilities. But by assuming that all voters have the same 
internal scale, there is a normalization. Other utilities are 
proportional. An assumption is made that they are linear, though 
various distributions of utilities are used.)

(The second normalization: the voter considers all candidates on the 
ballot, including a write-in, if any. The voter assigns 100% to the 
favorite and 0% to the worst. Another variation of this would not 
include any write-ins. Again, other utilities would be presumed to 
fall in the middle somewhere, but that is actually a separate issue.)

(And how are so-called sincere internal utilities translated to Range 
Votes, when they are not at the extremes? There is no fixed standard. 
Approval-style voting could be, in ordinary usage of the term, 
"sincere." That is, the voter is saying, "I'll be about as happy with 
either of these, and about as unhappy with either of those." This 
does *not* necessarily mean that the voter has no measurable 
preference, if only given the choice of two. It does mean that the 
voter is more likely, perhaps, to stay home in a runoff, but that is 
not guaranteed.)

>and in addition to that accept the Approval style voting as a
>secondary less good option.

Depends. It can be better, it can be worse. My position is that it is 
up to the voter to decide. Approval style, *if done skillfully*, will 
maximize personal outcome, but it can also backfire. Do a study of 
what actually happens, perhaps look at my analysis of Range 2, and 
you can see. With a large number of voters, and accurate utility 
expression possible -- in Range 2 this requires that any middling 
candidate be exactly in the middle -- the Sincere vote has the same 
expected (average) outcome as the Approval style vote. But it has 
other benefits that do *not* show up in the personal expected utility analysis.

The sincere vote has less variability in outcome compared to the 
Approval Vote. I think in the list of possible vote patterns, with 
the sincere vote, there is one where you'd regret it, because the 
worst candidate wins when that candidate would have tied with your 
middle candidate, who then would have a 50% chance of winning. With 
the Approval vote, there are two such patterns, as I recall. But the 
average outcome for both strategies is the same. (The patterns are 
equally likely, so, essentially, it is twice as likely that the 
Approval outcome is maximally bad, and twice as likely that it is 
maximally good.)

>  With this I think we are back in the
>original claim that Range may create a mess if some voters vote
>sincerely (and maybe are guided to do so) and some strategically.

No such mess has been alleged specifically. Rather, Juho and others 
continue to claim that a mess is created, but not *specific* scenario 
that deserves the name is mentioned.

The discrimination, in Range, between "sincere" and "strategic" is artificial.

Suppose we have a pizza election. Two friends are choosing a pizza, 
using Range Voting. They express, with their votes, not only what 
they prefer, but how strongly. Certainly, the person who votes 
Approval style is more likely to get what he wants -- indeed it is 
guaranteed -- than the one who votes "sincerely." This is quite like 
two friends having a discussion about it. One says, I like Artichoke, 
but Mushroom is okay with me. The other says, wow! I *love* Mushroom 
and I *hate* Artichoke.

Which pizza do they choose? Routinely, in ordinary human interaction, 
we give precedence to strongly expressed preferences. Do we question 
the sincerity of these preferences? We may, if voting over time shows 
a pattern. But who is to say, even then. A person's preferences may 
change. If a person always expresses strong preference, we may think 
them histrionic, but usually we will treat their preference as 
strong; however, in some cases, we may also start to treat our own as 
strong, if we never get what we want.

It balances out. And I expect the same with elections.

The alternative to considering preference strength is to use a ranked 
method, which can be truly lousy for choosing pizzas. Why would we 
expect better with public elections?

Only because we assume a polarized environment. Fine. If it's a 
polarized environment, most people will vote Approval style. But this 
actually gives control to those in the middle! (Polarized political 
environments *tend* to be polarized about the middle, so swing voters 
carry the day, and swing voters are quite likely to vote intermediate 
outcomes.)

There is a huge amount of discussion on the topic of "strategic" 
voting in Range, nearly all of it starting with an assumption that a 
mixture of strategic and sincere voting is somehow harmful. No proof, 
no demonstration, or only some contrived example, at most, that 
actually doesn't show harm beyond what is obvious:

In Range the preference of a majority can be passed over for the 
broader satisfaction of the whole electorate, including a minority 
with a stronger expressed preference.

*This is not a problem,* unless you consider the Majority Criterion 
sacred. And we fix that problem with detection of the condition, 
holding a runoff in the rare circumstance that it occurs, so that the 
consent of the Majority becomes explicit, thus satisfying the 
Majority Criterion where it counts: with the final result.

My contention is that usually the Range winner will prevail. This 
might not occur, however, if the majority understated its preference, 
or the minority overstated theirs. A runoff tests the strength of the 
preferences, and submits the final decision for majority vote, thus 
satisfying, fully, the principle of majority rule.

In a healthy society, the majority *often* gives up its first, 
personal, utility, in favor of a general overall utility. We wouldn't 
think it strange at all when a town votes to, for example, establish 
a fund for the indigent. This fund costs the taxpayers of the town a 
small amount, but makes a huge difference for those who need it. And 
this is, more or less, a zero-sum game (or even, because of 
administrative costs, negative sum). In elections, it is often not 
zero-sum, everyone can gain, and what the majority is giving up is 
maximized personal gain.

And in this case, because election follows election and people may be 
in different positions with each election, a distributed general 
benefit with each election will generally result in a greater 
personal benefit overall. You scratch my back, this time, I scratch 
yours, next time. Or vice versa.

A general increase in benefit is *generally* associated with a 
personal increase, overall, over time.

If you change the method to Approval, that larger general increase, 
under the circumstances of concern, can't take place, so *everyone 
suffers*. If it is Range, allegedly, those who vote sincerely 
"suffer," and this is a choice that they can make. Claiming that 
there is a problem is essentially asserting that voting stupidly can harm you.

And it can! No matter what method we have! Shall we remember that 
almost half the voters voted for Bush in 2000 and 2004? (It's 
undisputed in 2000, it is speculative in 2004.) I'm sure that, to 
them, it seemed like a good idea at the time.... but, as with the 
Iraq war, all the signs were there before the fact.