[EM] IRV vs Plurality

Abd ul-Rahman Lomax abd at lomaxdesign.com
Wed Jan 20 08:18:02 PST 2010

```At 03:01 AM 1/17/2010, robert bristow-johnson wrote:
>On Jan 17, 2010, at 12:53 AM, Abd ul-Rahman Lomax wrote:
>>
>>There is a common error here, which is to assume that Range
>>"requires" too much information from the voter.
>
>well, it does force the voter to consider the questions "oh, i hate
>this guy 28% more than i hate the other guy, so how do i rate each
>candidate in range?"

It "forces" no such consideration. If the voter thinks that thought,
the voter has far more quantitative information than is probably even
possible. All that Range Voting is is an allowance for fractional
sorting the candidates into rank order or into ranked sets, the
simplest being "approved" and "disapproved." If that's all the voter
wants to do, done. Vote max for approved and min for disapproved. And
the approved set may be one candidate or none.

(When a majority is required, voting against all candidates is not a
moot vote. It is a vote, generally, to hold a runoff or maybe even to
reconsider the entire election, is this office necessary to fill?
Sometimes we forget that public elections are not the only
application of voting systems!)

All the voter is doing is distributing voting power. It can be
distributed in a very simple way or in a more complex and
sophisticated way. It is up to the voter, and every voter has one
vote, and one vote only, and may exercise the whole vote or just part
of it. Voter freedom. I'm amazed at how many people object to it.

>   the range rating values are a superset of the
>adjacent integer rankings from a ranked-order ballot like one for
>Condorcet, IRV, Borda.  in the ranked-order ballot, all the voter has
>to decide is who she would vote for in adjacent candidates: A>B>C.
>she doesn't have to decide how much more she likes B over C than how
>much A is over B.

That's true. But the voter can vote Range in quite this way. This
argument would amaze me if I hadn't seen it so many times. Range is
too hard for voters, supposedly. But, let's back up. I'm not
recommending diving into public implementation of Range immediately,
beyond Range 1, or approval. Which is simply Plurality with a freedom
to multiply approve. Why in the world would we want to prevent this?

Robert's Rules of Order doesn't allow, on written ballots, multiple
votes, it voids the vote. However, that seems to be an historical
tradition, and the only reason given is that the vote must be an
error. How can they count the vote if it's an error. And it's an
error because it won't be counted. It's possible that there was, at
some point, some thought that it would violate one person-one vote.
But it is no more a violation of that, than is preferential voting,
which allows casting more than one vote. In the end, the voter has
only one vote to cast in each pairwise election. Plurality requires
that the voter cast all these votes with only one preferred
candidate, and to abstain from voting in all other pairs.
Preferential voting allows the voter to vote in different pairs (but
the voter can generally vote it just as Plurality), but most
preferential voting implementations don't allow equal ranking, which
is an obvious defect.

If rating is supposedly so hard, why don't we notice that requiring a
voter to rank when the voter has no significant preference is also hard?

Very simple to vote Range if the number of ranks is equal to the
number of candidates, i.e., it's a Borda ballot and is counted like
Borda. And the only thing that makes Borda different from Range is
that generally Borda doesn't allow equal ranking. Why not? The reason
give, supposedly, is to prevent "strategic voting," but that's a
defective concept applied to Range. Strategic voting, boiled down, is
a method whereby voters attempt to use the method to gain a preferred outcome.

That's what we want voters to do! The goal of a good voting system is
to allow their natural preferences to accomplish this, and if a voter
wants to vote "Anybody but Joe," why not?

Various Borda rules have been proposed as to how to treat incomplete
ranking (and equal ranking, if allowed by the ballot design, is
considered incomplete ranking). To me, the offensive way is to
devalue the ballot. That is, the ballot isn't given full value for
the highest rank, or, alternatively, minimum value for the bottom
rank. The effect is to weaken the vote. Why? Why should a voter who
decides to vote no preference between two candidates be assigned less
voting power in all the *other* pairwise elections?

Very simple concept. Allow equal ranking. It makes just about every
voting system perform better. It helps Plurality find majorities, to
the extent that voters use it. Supporters of no-hope candidates may
use it, thus showing, in the election, true support for their
candidate (because those votes are now unconstrained by a desire to
cast an effective vote for election purposes).

Sure, simple Approval has a problem, but only by comparison with
preferential voting. Not by comparison with Plurality. Since it's
practically free, just Count All the Votes, implementing approval
should be a no-brainer. Just about every voting systems expert agrees
with this. It would make IRV work better. Consider the Favorite
Betrayal problem of the Burlington Republican voters. Because they
are not allowed to rank both their favorite and the Democrat in first
rank, to improve the outcome ("strategic voting!") they must reverse
preference. If equal ranking were allowed, they have a better choice
than simply voting insincerely. They can vote for a set of candidates
in first rank instead of just one. If they did so, it's quite
possible that the Democrat would have won in the first round, with a majority.

But this is the obvious problem: they would greatly prefer to cast an
effective vote and to express their preference, and they have a
significant preference. Hence Bucklin. Instant runoff approval
voting. It much more closely simulates repeated election than any
other method, except my proposed Range/Bucklin, which does the
"repeated election" thing more precisely.

I've put a great deal of time over the last years studying these
systems, and, in the end, what I see is how to simulate the
sophisticated process of repeated election, in all cases except where
the voters simply haven't enough information to find a majority in
the first ballot. Making a decision without that majority is
dangerous, that's why it is avoided in peer organizations. With a
good system, however, the process can be limited to two elections,
with a plurality result in the second election being rare and still
very likely to be the optimal result.

Range advocates, in general, haven't understood the importance of
majority. They think that the Range equivalent of a plurality
election is sufficient, because, after all, isn't it theoretically
optimal? Sure. If the voter utilities are efficiently and accurately
expressed, the result is the best that could be found at that time.
However, in deliberative process, no decision would be made yet. The
process would be iterated, and iteration is not merely voting again
the options. The *whole*  process is repeated. Candidate elimination
isn't done, but, in fact, in deliberative process, candidates
withdraw, and new ones may appear.

I'd really like to see activists understand this basic process, how
it works -- and how well it works -- and then understand that a good
public voting system would approach this, simply making it more
efficient. Narrowing the field to two candidates greatly helps the
electorate focus on a choice. But because there is no way to
absolutely guarantee that the two best choices enter a runoff (which
is what it now becomes, rather than a repeated election), there
should be an escape hatch, a way to fix the problem of poor choice of
top two. There are two approaches:

1. Choose a better top two than a plurality primary finds. Generally,
there are two kinds of natural winners: the Condorcet winner and the
Range winner. They will usually be the same. But when they are
different, and if the votes were accurate expressions of utilities,
the Range winner is better. But if the Condorcet winner is different,
the electorate has not specifically consented and has in fact voted
against the Range winner. This is a question to be presented to the
electorate in a runoff, and there is a peculiar phenomenon which
voting systems students, focusing only on single-ballot deterministic
methods, overlooked: turnout. If the runoff is a special election,
making voting a bit more inconvenient, preference strength is tested
in a way that can't be faked. This favors (greatly) the Range winner.
The other effect that has been overlooked is that in general, a
majority will give up its first preference, voluntarily, if the
preference is weak, in order to satisfy a minority with a strong
preference. Isn't that what we'd expect our neighbors to do for us?

2. Allow write-in votes in the runoff. Normally, this will be moot.
But suppose some serious error is made in the primary? Case in point:
IRV winner in San Francisco wasn't eligible for election. Not
discovered until after the election. Would have come out, almost
certainly, in a runoff, where there is then focused attention. Okay,
it's found before the runoff. What can the voters do? When there is
another candidate with strong preference over both candidates on the
runoff ballot, a write-in campaign can succeed. But it can be
dangerous, what if it causes a spoiler effect? Hence a spoiler-free
method should be used in the runoff even if there are only two candidates.

When San Francisco outlawed write-in votes in the runoff, apparently
the argument was that the voters had been promised a majority.
However, the solution to that problem isn't to force a majority
arbitrarily, that then becomes a faux majority. There really are only
two reasonable options: repeat the election yet again, or accept a
plurality. In this case, if a good method is used for a runoff, and a
write-in causes majority failure because of bullet voting, accepting
a plurality would almost always be adequate. In peer organizations
running under Robert's Rules, a different choice is made: repeat the election.

>   one is a quick set of qualitative decisions.  the
>other makes it a quantitative issue, and that's when a lot of us get
>out our dartboard.

Dartboards are fine. However, if you need a dartboard to select
between two candidates, equal ranking is more accurate and actually easier.

Start thinking of voting for or against *sets* of candidates. It all
gets much easier.

>   i don't think making threshold decision based on
>the precise sum of a bunch of noisy numbers (which is what Range is
>when we use our dartboards to score a candidate) does much other than
>to add the means of the noisy numbers and a sum of zero-mean random
>numbers which throws a little bit of dice into the mix before using
>the threshold comparison and determining the winner.

Your "think" isn't supported by the simulation data. Don't you agree
that voters will *on average* rate candidates they prefer higher than
candidates they don't prefer? These aren't random numbers, they are
voter expressions which are naturally based on underlying utilities.
And the simple expression of Yes or No on each candidate fits fine
into this. And if a voter only wants to vote for the favorite and
against all others, that fits fine too and is actually an effective
vote, if it's for a frontrunner, which covers, by definition, a large
set of voters. This is overlooked: only a few voters need finer ratings.

But, in fact, many voters will add lower preferences, showing support
for certain minor candidates. That's why Range has what Warren calls
an "incubator effect," allowing the true support for a candidate to
appear long before actual election is possible.

But Bucklin is simpler at the outset. The design of Bucklin was
brilliant, at least Duluth Bucklin, the one used in the election
reversed by Brown v. Smallwood.

Three rank ballot. Equal ranking was allowed in third rank. This is
an approval ballot, in fact, and I would allow equal ranking in all
ranks, for reasons I've given. If a voter has a significant
preference, there is no reason to equal rank in any rank but the last.

I say it is an approval ballot because every vote is an approval
vote. If you are not willing to support a candidate's victory, you
don't vote for the candidate in any rank. It's an approval ballot
that categorizes candidates into three ranks, I'll call them
Favorite, Preferred, and Acceptable.

If there is a runoff if no majority is found, the meaning of
"Acceptable" is clear: it means "I would prefer to see this candidate
elected than see a runoff held." That's a binary choice, Robert.
Binary choices are the simplest to make. Easy? No.

Favorite should be easy, and allowing equal ranking makes it a bit
easier, by covering the case where there are really two favorites,
without strong preference between them. In this case, equal ranking
is sincere and is strategically more effective as to maximizing
probable outcome.

"Preferred" isn't really necessary in elections with relatively few
candidates. "Relatively few" means not 23, as in San Francisco, or a
hundred, as in one of the early Bucklin elections. (People got
excited by the first use of the method in the town, and lots of
people filed. That wouldn't continue, but generally preferential
voting encourages more candidates.) But the method must be able to
handle any number of candidates.

The only "hard" division is between Preferred and Acceptable. And my
suggestion is that most voters would leave the Preferred category
empty, unless they can naturally find a candidate or candidates to
put in there. Better than merely Acceptable, but not Favorite yet.

Voters should know that in many elections where there are more than
one or two serious contenders, all the votes will end up being
counted, so the election will become a pure Approval election. Don't
vote for a candidate if you aren't willing to be counted as a
supporter. With a Range ballot used for Bucklin analysis, you'd be
able to express precisely low high or low that support is, if you want.

Voting isn't easy because it is an exercise of power. Answering polls
is easy, because it's just an opinion, there is little or no responsibility.

>so it requires thinking that we wouldn't have to do otherwise.

Forget it, then, Ask voters to think? Horrors! We all know voters
can't think, right? I've actually found this opinion common among
voting systems activists. It shows up especially in how voting system
political action groups are formed. They don't use democratic
organization, they use tight-control central oligarchical control.
They don't trust democracy. The Center for Voting and Democracy
didn't trust democracy. I just love that kind of irony.

Actually, and ballot instructions and pre-election voter education
should make it clear, a range ballot *allows* refined expression, but
doesn't require it. As long as one votes max, or close to it, for a
preferred frontrunner and min, or close to it, for the worst
frontrunner, the vote has quite as much power as every other vote,
and all other expressions are purely voluntary, allowed expression,
not required in any way.

Therefore the voter, with respect to all these other votes, for
non-frontrunners, is free to simply make a guess. Those guesses,
amalgamated over many voters, will be quite accurate as to social utility.

As has been pointed out, a range ballot with sufficient resolution
can be voted Borda, it's a reasonable vote, and if it isn't, the
voter can surely see that and shift the votes as needed to make it
work. Leave the favorite and worst at the top. Move frontrunners
toward the extremes (or all the way there). And then let the rest
fall where preference order implies. Very simple to do. Not
difficult. And strategically effective. And sincere.

Never reverse preference order with Range, it never makes sense, it
can only harm the outcome, never improve it. This is why Approval was
proposed by Steve Brams as "strategy free." It was, according to the
definition of strategic voting in use at the time, it meant
preference reversal. But proponents of other systems attacked this,
by redefining strategic voting (without ever specifying that they
were doing it), as meaning equal ranking when there was "actually" a
preference. No. Approval voting is a division by the voter of the
candidates into two separate sets, and the method never rewards an
insincere division. (This would mean that the division reversed
preference order for two candidates.)

Because voting systems theorists lost sight of the *function* of
voting and got lost in the abstract theory of what makes an "ideal"
system -- at the same time as they contended that there was no ideal
system -- some of them missed the boat, which resulted in all sorts
efficiently find socially optimal results.

Many even asserted that there was no such thing as a socially optimal
result, confusing an underlying reality with the difficulty of
measuring or determining that reality in real situations, i.e., real
and commensurable personal utilities. But in some real situations, we
actually can determine these. Further, in simulations, we can
postulate them and, then, for a large series of simulated elections,
determine voting system performance, usin various models of voter
behavior consistent with the underlying absolute utilities. Many
misinterpreting Arrow's theorem, neglecting the work of Dhillon and
Mertens showing that there actually is a unique optimal system
satisfying reasonable versions of Arrow's axioms. Hint: Range Voting,
which they called Rational Utilitarianism when used according to a
particular strategy, voting von Neumann-Morganstern utilities, which
are optimized Range votes. And it works with Approval.

Warren Smith has done yeoman work in the study of simulated
elections, and the models of voter behavior could be improved and
made more sophisticated, with factors such as turnout being necessary
to apply this to runoff voting. (Runoff voting has been studied, but
only primitively, assuming an immediate repeated election with the
same voters and same set of absolute utilities, which is utterly
unrealistic. Runoff voting outperforms the simulation results because
of these other factors.)

>   if we
>don't feel like thinking that seriously, it becomes a big noisy
>threshold on the means of stable ranks.

Rank data is actually noiser, because of the suppression of
preference strength information.

>   that's sorta like Borda and
>does become the equivalent if people's evaluations of candidates
>sorta "linear".

It's been shown that with a universe of candidates that covers all
possible positions, with the appropriate distribution, Borda and
Range are equivalent. The distribution is such that the rank distance
of two candidates indicates the preference strength. There are
Condorcet methods which use assumptions about preference strength,
but it's very noisy when the number of candidates is small.

>>First of all, Approval is Range, simply the most basic Range method.
>
>it's Range with 1-bit binary values.

I.e., Yes/No.

>>So what you have is a contradiction: "Range" requires both too much
>>and too little information. Surely it depends on the specific Range
>>implementation.
>
>yes it does.   of course the answer is (if i may appeal to an audio
>image) that what we *normally* mean when we say "Range" is were the
>sliders for each candidate are either continuous or have many
>discrete values (say 10 or 100).

Nobody is proposing continuous rating but Warren. Only a
mathematician. In fact, our preferences are not as precise as all
that. There isn't much good reason to use more than, say, 11 slots,
unless there are a lot of candidates. But remember my suggestion. We
Next step up is Bucklin, and the desirability of allowing ranked
approval is so great that the step might be direct, plurality -> Bucklin.

But if a jurisdiction already has runoff voting, which is quite
sophisticated and which should not be dumped, then the first step
would be Approval Runoff, no cost, no brainer, might reduce runoffs a
little, or Bucklin/Runoff, using Bucklin for primary, and, if
write-ins are to be allowed, which I highly recommend, for the runoff
as well. The cost is very low.

>a two-position slider is what we call a "switch". requires one bit of
>information.  that's getting qualitatively different.  either you are
>at the minimum number of levels (or bits of information in the slider
>position) or you're not.
>
>perhaps a 3-position slider can be "Actively Disapprove", "no opinion
>- neutral", and "Actively Approve"

Sure. In fact, the first step beyond approval would be Range 2, and
positive/negative is an obvious implementation that has coherent
meaning, pretty easy to understand.

>perhaps a 4-position slider can be "Actively Disapprove", "no opinion
>- neutral", and "Actively Approve" and "Hey, I really like this guy!"

I.e., Favorite. Now, consider Bucklin. "Neutral" is the meaning of
the lowest rank. It means "barely acceptable," actually. It means
"I'm not offended if this candidate wins, don't bother with a
runoff." "Actively disapprove is expressed by not casting any vote
for the candidate. "Actively Approve" is what I called "Preferred."
And then there is the Favorite. So the Bucklin ballot, designed about
a century ago, is this kind of ballot, and it works that way.

>[...]
>we can continue on like this with more discrete levels and all we'll
>get are gradations of the above.  it's all a matter of degree.

Sure. Why not start at the simplest, collect data, measure the
effects (using polling), and then slip it up a notch and see what
happens? At some point there will be diminishing returns. The only
cost of Range balloting is an increased number of slots (the same
with all preferential voting methods). There is no significant

(Some range activists disagree and want to use average range, which
to get people to just count all the votes. I'd suggest collecting a
lot of ballot data in real elections before advocating average range.)

>but the 2-position slider is a 1-bit piece of information:
>"No","Yes", that's the minimum a voter has to judge.  that's
>qualitatively different.  here's why:  with the multi-level (3 or
>more), then order has to be considered with candidates that you
>approve or disapprove.

"Has to." Stop it! The slider does not force voters to consider order
unless they want to. If they want to, they will find it easy to
order. If they don't find it easy, don't order! "Not finding it easy"
means low preference strength, hence ordering just makes noise.

>but the multi-level or continuous slider (3+) requires *more* than
>just ordering information (who is preferred to whom?), it requires
>*spacing* information.  like "i hate candidate D worse than i hate C
>whom i dislike more than B whom i like less than A."  you have to
>decide that D is twice as badder than C than C is badder than B or
>some other value judgement.  what if you just don't feel like making
>such a precise judgement?  then you get your dartboard.

No, you lump candidates together when you have difficulty deciding
rank order. See, the very difficulty is useful information, simply
expressed by equal ranking. So you end up with sets of candidates
easy to distinguish from the others, but difficult to divide up. That
will then generate optimal results if everyone votes that way. And
why wouldn't you vote that way? It is, in fact, the easiest way to vote!

Bucklin doesn't require you to make the much more difficult strategic
decision, except for the raw decision to vote for a candidate at all.
That you sensibly make strategically, i.e., you might hold your nose
and "approve" a candidate, because you believe this is the best
frontrunner. And if you don't like that, get politically active and
work to get better candidates on the ballot and into the lead!

Think about it! Sort candidates into four categories, as you
described. Favorite should be easy, if not, approve more than one
favorite! Don't put the favored frontrunner in here just because the
candidate is a frontrunner, rather just make sure that you vote for a
frontrunner somewhere, that's the only decision you need make.

I'm suggesting that the middle category, "preferred," be left empty
unless there is a clear candidate or set of candidates for it. These
should be candidates who are better than average, you would actually
be pleased with the election of this candidate, even if you also have
a different favorite.

So the only "strategic" category, requiring some heavy lifting, is
the lowest rank, and, there, you are making one of two decisions,
depending on whether or not the election is final or it is a primary
in a runoff system.

1. If deterministic, plurality will prevail after all the ranks are
collapsed, vote in bottom rank for any candidate who meets or exceeds
your expected outcome. This can mean the best of two evils, maybe.
Maybe not. Maybe it's better to let majority failure speak for
itself, and not pretend support for what you actually oppose. And
then why not work to get better candidates on the ballot and to
develop wide consensus on their quality? If this is deterministic,
perhaps it's a runoff itself, then, if the two candidates on the
ballot are that bad, why not vote for a write-in, like voting for a
candidate named Mr. "Both Assholes." Legal vote, and if enough people
vote that way, it will cause majority failure. Better, when you saw
this election coming, why didn't you help get a write-in campaign
going. On the other hand, if you know that your opinion is isolated,
that most people do, in fact, prefer this set of two candidates, a
write-in campaign is a waste of time and money. You'd know this, in
fact, quite well, from the primary data. The first and second rank
votes are clear indicators of positive support, you would never put a
best-of-two evils candidate in there.

2. If majority is required, the third category, Acceptable, is pretty
easy. Would you prefer to finish the election with a candidate? If
so, vote for the candidate. If not, don't. It's expected that primary
votes are more conservative, i.e., less likely to be compromises.

>r b-j                  rbj at audioimagination.com
>
>"Imagination is more important than knowledge."

They are both important. Knowledge without imagination is dead.
Imagination without knowledge is useless.

Take a Bucklin ballot. Score it this way: Favorite 4. Preferred 3.
Acceptable 2. No vote 0. See what happens.

There is only one piece of information missing from this ballot,
which is score 1. That means "Disliked." And then, no vote is 0 and
means "Worst," but if 0 is explicit, then no vote means "no opinion"
and 0 means "No," seriously disliked.

In a runoff, "disliked" information might be particularly useful.
Range advocates would say, generally, that this less-disliked
information should be used to determine winners, other things being
equal. I'd agree, if there is no other option. If the information is
there, it could be used to test whether or not there is a difference
between a social utility maximizer (based on expressed votes) and the
approval winner. I'm not sure how much is gained, probably a little,
but we will know much better when there is good basic data from
Bucklin elections (or approval elections or Range elections).

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