[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
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
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
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.")

```