[Election-Methods] utility theory lesson for a very confused

Abd ul-Rahman Lomax abd at lomaxdesign.com
Wed Jan 9 12:59:32 PST 2008

At 03:50 AM 1/7/2008, Don&Cathy Hoffard wrote:
>Abd ul-Rahman Wrote:
> >The Range vote is a red herring, the same 
> objection would be made if this were an 
> Approval election with votes of 1/1/0 for ABC 
> from Clay and 1/0/0 for >Don. Don would then 
> complain that he did not get to cast a vote for 
> C. But he did have the opportunity to cast that vote:
> >initially, and he chose not to cast it.
>You just took away my right to vote.

No. You still have one full vote. You don't have 
more. You may cast up to one vote in each 
pairwise election, but you cannot cast a sum of 
more than one vote across a series of pairwise 
elections. This is general Range theory, though 
it usually is not stated like this. It becomes 
obviously interesting if you look at utility 
analysis and at votes as bids. Every voter has a 
fixed amount to bid, for each candidate.

Start out with plurality. You do not have the 
right you claimed. If the status quo were, say, 
IRV, which does allow such multiple votes (or any 
Condorcet method, better), you might well 
complain. However, there is some legal opinion 
precisely that those are violations of one-person 
one-vote. I'm not necessarily agreeing with that, 
but if we, again, look at an election as an 
auction, this is indeed what is happening.

You have the sum of $1.00 to spend in an 
election. You are bidding on the election of 
candidates. If A is elected, you will consider 
your $1 well spent. If C is elected, it's worth 
nothing to you. How much is B worth? The election 
method is going to measure the total "worth" of 
the election, as determined by the voters in 
their sovereign discretion, and award the victory 
to the candidate who maximizes it. You can bid 
any amount you like (let's say, though, in 
increments of one penny) for each candidate. If 
you make no bid, it will be assumed that you have 
bid $0.00. (This is sum-of-votes, not average 
range, some Range advocates think Average Range 
is better, I think it is actually an error.)

Except, of course, it is not your money you are 
bidding. It is the tax money, and it has been 
decided to give every voter 1.00 vote (call this 
1 equal share of the total voting electorate) to "spend."

If A>B is worth $1 to you and B>C is, you claim, 
worth $1 to you, then you are trying to spend $2. 
That is, you will bid $1 higher for B than A and 
$1 higher for B than C, so you should want to bid 
$2 for A over C. But you have only $1. So, if 
those relative utilities to you are accurate, you 
would bid 1, 0.5, 0. This means that you have a 
strong preference for A over C, compared to the 
preference for A over B and B over C.

>You say I could have voted for C by voting for 
>(A>C>B) 1/1/0 (But if I did that I can’t vote for A over B).

That's right. Try that trick with Plurality. 
Approval gives you an additional choice, it does 
not take one away from you. Simply Count All the 
Votes, and you get a relatively advanced election 
system that solves the serious first-order 
spoiler effect, at no cost. Want something 
fancier? Sure. But whose money are you going to spend for it.

Under current conditions in the U.S., the 
likelihood of a third party candidate winning a 
major election is close to zero (unless by 
serious vote-splitting, which is another problem, 
one where IRV can fall on its face. Approval 
would normally handle it -- but that's not the 
point here). (In nonpartisan local elections, 
it's another story, that too is a separate 
topic). In nearly all elections -- even local 
nonpartisan ones, there are usually two 
frontrunners, rarely more. Now, suppose your two 
favorites are the two frontrunners. How you vote 
under Approval depends on the preference 
strength. If they are really the same to you, 
vote for both. Why not? But if there is a 
significant difference, vote for one. That's 
extraordinarily easy, I'd suggest. What about the 
third? *It doesn't matter*. If you like the third 
as well, what a lucky voter you are! I've never 
been so lucky. (Except maybe in an upcoming primary....)

But what if you favor the third party candidate? 
Again, it's easy. You vote for the third party 
candidate, and whether or not you vote for one of 
the frontrunners depends on whether or not you mind being irrelevant.

As far as what *I* would do, you could indeed 
have your cake and eat it too. That is, I would 
not hold a simple approval election. I'd have an 
extra position for each candidate called 
"Favorite." If there is a candidate with a 
"Favorite" vote that beats the Approval winner 
(favorite is for this purpose the same as 
"approved"), there would be a runoff. I'd also 
hold a runoff whenever there was majority 
failure. A real runoff. Why? Well, there are 
easily shown situations where the first 
preference of a majority will be *rejected* by 
the majority if they know how the other voters 
feel. Further, a runoff tests preference 
strength. It gets clearer with Range Voting. If 
the majority preference is strong, to sum it up, 
the majority will turn out to vote in the runoff. 
If it is weak, they really don't care, they will 
tend not to turn out. It's a *rough* Range test, 
and it satisfies, in fact, the majority criterion 
under all definitions I know of.

>With my vote of (A>C>B) of 10/1/0 I am saying 
>that I do have preference for C over B.

Yes, you do have a preference. Confusing way to 
state it, by the way, changing the sequence of 
the votes. I did not state that you couldn't 
state that preference, I said that I think most 
people won't bother, and I wouldn't. How would I 
feel if that one tenth of a vote for C put C over 
the top to beat A? Probably not good! But what I 
would actually do would depend on preference strength.

>With Approval voting you are not allowing me to 
>vote for a candidates that I like better than another.

Not in multiple pairwise elections. Approval 
gives and takes away. Compare it with Plurality, 
not with higher resolution Range! (higher 
resolution Range is better, but the remaining 
question is whether or not it is worth the extra 
ballot space and voter effort. Probably, but will 
the voters buy that? If so, great. But getting 
Approval is hard enough. Get approval, and higher 
resolution Range methods will become a very 
obvious next step. Approval with fractional votes allowed.

>You also took away Clay’s right to vote.
>Clay can vote (A>B>C) 1/1/0 for A over C and B 
>over C but you are saying (with approval) that he can not vote for A over B.
>He also indicated a preference of A over B with (10/9/0).

A slight preference, and it might make a 
difference if I have my druthers and there are 
runoffs whenever majority preference is not 
clear. I'd want to see an approval cutoff in 
Range elections, a vote above a certain level is 
an explicit approval. It is the voter saying that 
the voter would vote Yes on the question "Shall 
this candidate be elected," preferring that 
election to further delay. Just as an Approval vote is such a Yes.

>(assuming 4 candidates(A/B/C/D))
>Now Plurality voting is limited to the following:
>(1/0/0/0) or (0/1/0/0) or --- to (0/0/0/1)
>Approval voting is limited to the following:
>(0/0/0/0) or (1/0/0/0) or (1/1/0/0) or --- (1/1/1/1)
>This is clearly better than Plurality 
>voting.  You have a lot more chances to express you opinions

Yes. You lose the right to participate in one 
pairwise election, with one vote, but gain the 
right to participate in all the other pairwise 
elections. With three candidates, it's a gain. 
With two it's moot. With more candidates, it is more of a gain.

>Preference voting is limited to the following:
>Voting for A>B (1/0) or (0/1), and for A>C (1/0) or (0/1) and ---- etc.
>In Pure Preference voting you have a ranking of 
>(A/B/C/D) states only that you prefer A>B and 
>A>D and they are treated the same.
>This method clearly provides more options for the votes than Approval voting.
>You may “Approve” of A and B but you still can have a preference of A over B
>It also encompasses Approval voting if A=B (1/1) voting is allowed
>A problem with Preference voting is that it does 
>not always come up with a clear winner.

There are different kinds of preference voting. 
Some *allow* equal ranking. Such systems are 
actually Approval plus ranking options, similar 
to Bucklin voting, which was actually quite 
popular in the U.S. for a time, it appears. I 
mentioned before how it came to be outlawed in Minnesota.

>  Range voting is limited to the following:
>(10/x/y/z) for A/B/C/D or any other combination (were x/y/z =< 10 and >= 0)
>This method allows the voter to “Quantify” his 
>or her Preferences. A>B (10/9),--, or 10/0)
>There are different forms of range voting, you 
>could used 10 but you could use 100 or 3 (3/2/1/0)
>Range voting provides the maximum (or closes to 
>it) flexibility (options) for the voter.
>Range voting however does add a lot more 
>complexities to the voting process, this makes 
>it more difficult to see the impact of ones vote.
>And there may be the Problem of adding individual quantified preferences.

Actually, Range voting is quite simple to count, 
and voters may, if they wish, vote it as Approval 
or Plurality. There is no need to add "individual 
quantified preferences" unless one wants to, it 
confers, under some conditions, a *small* 
strategic advantage to vote "sincerely," but more 
often, shifting the votes toward Approval style 
voting is individually optimal *if* one knows who 
is likely to win. It's obvious, really: put the 
voting power in the pairwise elections that count 
the most. If the method includes a pairwise test, 
as I've proposed, then one might vote 100 for a 
favorite and 99 for another, perhaps the 
preferred frontrunner. However, Range 100 is 
probably overkill. Do I really need to express 
votes in increments of 1/100 vote? I'd rather see 
lower resolution Range with a Favorite marker 
that is optional to use. The favorite is used to 
show just that, a favorite, but does not affect 
the Range vote, leaving one free to cast those 
votes without restriction. As I've mentioned, it 
could affect the outcome: if Favorite votes and 
equal approval votes at the top rank show that a 
particular candidate would beat the Range winner, 
there is then a runoff between such a winner 
(likely a Condorcet winner) and the Range winner.

This kind of procedure is quite analogous to 
current practice in many jurisdictions of 
requiring a runoff when a majority has not expressed its preference.

>A question voters need to ask is “how much added complexities do they want”.
>Plurality has been with us for a couple of hundred years.

Approval has been with us for a long, long time. 
It was used as part of the election of the Doge 
in Venice for *five hundred years*. It was used 
for hundreds of years, with a supermajority 
requirement, to elect Popes. It really is an 
obvious variation on Plurality (and may be used 
to elect by a plurality, which I dislike ... but 
still better than single-vote Plurality), one 
that simply counts all the votes. And I have 
*never* seen a good argument for not doing that, 
it's just been assumed, for a long, long time, 
that this is the way to do it. Robert's Rules 
instructs the clerk not to count overvoted 
ballots because they are "errors" and the 
"intended" vote can't be determined. In other 
words, the reason we don't count them is that 
they are errors and they are errors because the rules say not to count them.

Plurality will *usually* choose the right winner, 
if there has been enough deliberation. What I've 
seen is that Approval can get there faster. A 
really good method is an Approval poll followed 
by an election by ordinary motion. I.e., there is 
a poll, and then someone moves "I move that we 
elect Mr. Approval Winner." That's open to 
amendment, like any ordinary motion; all votes 
are Yes/No until a majority is obtained. This 
method is Condorcet compliant, the only problem 
is that it can require a series of votes on 
various amendments and on the question of whether 
or not to proceed to a vote (typically a 2/3 
majority required for that). But deliberative 
methods also incorporate, in actual practice, 
preference strength. Note that a minority can 
block the election, so there is a way that a 
strongly motivated minority can prevent the 
election of a disliked officer, thus compromise 
is encouraged so that officers enjoy broad 
support. Obviously, this works, it's been used for a *long* time.

But a truly advanced method is also one of the 
simplest: Asset Voting. We'd thought until 
recently that it was invented by Warren Smith a 
few years ago, but, in fact, Lewis Carroll 
proposed it in the mid-19th century. Ideal for 
proportional representation; it's a trick. It's 
not actually an election in the ordinary sense, 
there need be no losers, though there are those 
who must compromise in order to be represented. 
There are ways to use Asset to implement a hybrid 
direct/representative democracy that avoids the 
hazards of each and probably brings the benefits 
of both. The basic idea of Asset is that you vote 
for anyone you choose. You can, in my 
interpretation, vote for yourself (you might be 
required to register as available). No votes are 
wasted because the candidate(s) who receive your 
vote may reassign it at will, the votes are 
"assets." In my simple version of asset, the 
ballot is an Approval ballot. If you cast more 
than one vote, your vote is divided up among 
those you vote for. Most people, looking at this 
for the first time, don't get it, as far as I've 
seen. They apply the assumptions of 
plurality-driven politics to Asset. There aren't 
any losers in Asset, the only people who don't 
find *chosen* representation are those who, if 
holding votes, are not willing to make the 
necessary compromises, plus those who voted for 
them. Note, also, that if someone gets more votes 
than the quota necessary to be elected (which I 
would make an *exact* quota, not the Droop 
quota), the excess votes are redistributable 
assets. As well, distributors of assets may 
assign votes in precinct blocks, *thus creating 
virtual districts*. If you voted in such a 
precinct, then, you would know exactly who your 
personal vote elected. (to high accuracy; because 
of the necessity of some slop in block 
assignment, it might be 99% of your vote that went to a winner.

But, frankly, it all starts with Approval. Very, 
very simple method, very easy to implement (just 
strike a few sentences out of the election code), 
considered a quite good method by experts (*not* 
perfect except according to a few), ancient and 
honorable history, easy to vote (if you are a 
major party supporter, you can quite cheerfully 
continue to vote as you did before, it's probably 
your best vote anyway). Let's see, what's wrong with it?

Well, it isn't perfect. If you are one of the few 
percent of voters who support a third party, it 
still leaves you with a choice: do you vote only 
for your favorite, or for your favorite *and* a 
preferred frontrunner? But that's a vast 
improvement over the current situation, and for 
everyone else, pretty much, it's no big change. 
Major party supporters may also decide to cast 
votes for third party candidates, to encourage 
their party to move in that direction. However, 
they would need to be aware that if enough voters 
think like them, the third party candidate could 
win. If they wouldn't like that, I wouldn't suggest doing that....

The compromises that Approval "asks" the voters 
to make are essentially the compromises that 
*society* must make in order to have elected 
officials with broad support. Approval certainly 
does not guarantee majority support (unless that 
is required by the rules), but it makes it easier 
to get there, quite possibly more efficiently 
than the commonly-proposed and much more complex 
and expensive Instant Runoff Voting.

Bucklin is also pretty simple, easy to count and 
understand, and allows enough ranking to probably 
satisfy nearly everyone. In the classic Bucklin 
implementation, the third rank was a full 
approval rank with no overvoting restrictions. 
There were two single-vote ranks above that. I 
would allow all ranks to have multiple votes, I 
see no reason to toss the vote of someone who 
thinks that A and B are equally good.

>If you ask voters to change to any of the other 
>methods above most would say “No way– all I want to do is Vote”

I'd say, "Let them, and count all their votes." 
What ever made us think that we needed to do anything else?

(Approval is sometimes thought to violate 
one-person, one-vote, but, in fact, only one 
vote, at most, cast by an Approval voter ends up 
being effective -- or none are effective. The 
ineffective votes are all moot, they could be 
struck from the ballots and the outcome would not 
change. Only a vote cast for a winner is 
effective, in the end, and only one of those is 
allowed. The restriction becomes, "A voter may 
cast as much as one vote, and no more than one 
vote, toward the election of any candidate.")

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