[EM] Some brief campaign argument (Approval)

Martin Harper mcnh2 at cam.ac.uk
Tue Apr 17 09:02:39 PDT 2001

I'm concatenating my responses to all three posts in this one.

I'm comparing Approval to Condorcet in this message. I reckon most people on
this list would say that even if Approval is worse than Condorcet, it's still
better than IRV, Borda, Plurality - if you believe otherwise, please do say so -
privately or by list, I don't mind. Here and in the rest of my post, by
"Condorcet" I mean whichever Condorcet method the reader thinks is the best: the
details aren't critical.

Oh, and I'll be offline for a couple days, so I may not respond to emails and
such for a while. Real Life is a horrible thing, is it not?

To summarise...
1) I reckon Approval strategy is pretty simple if you don't care about finding
the *perfect* strategy.
2) When polls are bad, the election becomes 0-info, and Approval should still
find a good winner.
3) Approval doesn't comply with the Condorcet Criterion. But the Condorcet
winner is not necessarilly the best candidate from an social utility
perspective, so that's not necessarilly a bad thing. Depends on what you desire
in a voting system.
4) Approval votes, in general, are just as likely to be instrumental as
Condorcet votes.
5) The complexity of finding a good strategy in Approval is offset by the
complexity of finding a complete sincere rating in Condorcet. Personally, I
think Approval wins the comparison (but I would, wouldn't I?)

LAYTON Craig wrote:

> There seem to be three main reasons for believing Approval is the best
> electoral method - 1) a sincere vote is always the best strategic vote; 2)
> approval elections will elect a higher SU winner than any other method/s in
> a real world scenario.
> (There may be a further reason, that approval is the most mathmatically
> consistent method, but on its own, I don't find this argument persuasive.
> Please let me know if you do, and why.)

I hadn't even heard of this one - I'd kinda be interested to hear it...

> 1) Approval is unique in that a sincere vote is always the best strategic
> vote.  However, this is because you are only allowed to express a single
> layer of preferences - if you're preference is A>B>C, you can only express
> the preference A>B or B>C (in addition to A>C).  If you choose to express
> A>B, the system forces you to express B=C, even though this may be far from
> your sincere preference.  It is only a severe restriction on the preferences
> you can express that gives Approval this property, so I don't see it as an
> advantage.

I see it as an advantage in the area of simplicity - rather than seeing sincere
voting as necessarilly a good in itself. If there are n candidates then there
are n-1 different strategical votes to consider. If it was possible for the best
strategic vote to be insincere then there would be 2^n different strategical
votes. Ideally, we'd like a method which only had a single strategical vote that
needed consideration, so that voters could just vote that without thinking or
being worried about other people's strategy. However, that's not an available

> 2) Issues of Social Utility
> In a country with plurality voting, approval
> might not change voting habits at all and the vast majority might continue
> to vote for just one candidate.

A country which just changed from Plurality voting is likely to retain, at least
initially, its two-party system. This will happen whatever election method is
chosen. In a two-party system, those who support one of the major parties as
their first choice would be correct to vote simply for their major party. In the
absence of any other info, this is their best Approval strategy.

Those who supported a third party in Plurality are likely to be very familiar
with the problems of spoilers and such. The strategy of voting for the better of
the two frontrunners, and everyone they prefer to that candidate, is their best
Approval strategy. This is no more complicated than the Approval strategy the
majority of them use anyway.

It will take time for a two-party system to die and turn into a more multi-issue
multi-facted political climate - probably an election or two. I've got no
evidence or such for this, but my gut reckons that after an election or two
enough of the voters will have a handle on an Approval strategy which is good
enough to ensure a better SU than Condorcet. After all, even if they just settle
on "above mean" the results will still be better.

> Approval leaves the way open for "vote for everyone except X" type campaigns

It certainly does. If X=Darth Vader and he appears to have a genuine chance of
winning, then the presence of such campaigns is likely to raise the average SU
of Approval, not lower it.

Note that if X is not the worst candidate from your point of view then property
(1) above ensures that the campaign is unlikely to persuade you to vote for
everyone except X. It might, however, persuade you to disapprove X and everyone
worse than him.

> On the
> whole, I find no evidence to suggest that Approval will, on average, find
> the SU winner more often than a Condorcet system. The examples that "prove"
> approval will, are based on unreasonable assumptions.

I'm guessing that the unreasonable assumption is the assumption that voters will
use good strategy? (or alternatively, will use 0-info strategy)?

There are two problems/assumptions with the strategy issue, as I see it.
1) One faction may have a much better strategy than another, because they have
more motivated voters.
2) A significant number of the voters may use a strategy which not only is worse
than the 0-info strategy, but is so much worse that Condorcet starts getting
better expected SU.

The first case is regrettable. However, note that more motivated factions
already have an advantage because they are more likely to actually vote.
Approval is (arguably, see later) simpler to vote than Condorcet, so it will
have a better turnout, and from that point of view faction motivation will be
less of an issue. I'm not sure which will turn out to be the bigger problem:
differing turnout rates or differing strategy rates. I *do* note that, in
Plurality, commentators often note that such and such a party had greater
problems with turnout, but rarely note that such and such a party had greater
problems with its supporters failing to strategise. This leads me to suspect
that turnout is more party dependant than levels of strategy.

The second case I don't seeing as being a real problem: the 0-info strategy is
pretty simple, as is the "candidate you'd vote for in Plurality, plus anyone's
who's better than him" strategy. Heck, even "don't reverse preferences, and
choose how many to approve randomly" gets you better SU than Condorcet - I think
you'd need to have voters who were deliberately voting in a perversely dumb way
before you start having problems here.


> I left out number 3) which was approval's simplicity

And this, to me, is the most important thing Approval has going for it. Argument
(1) is only relevant because it makes life simple.

Specifically, the complexity added by having to look at polls and opinion to
play guess-the-leader is *much* less than the complexity added by having to look
at every manifesto in detail to determine your exact ordering of candidates.

> However, it isn't necessarily true that Approval is simpler to understand or
> to vote.  Sure, the instructions are simple (vote for as many candidates as
> you like), but it isn't easy for voters to understand how they should vote -
> for how many candidates, what's the best strategy, how should I be using the
> polling information etc.  I would have trouble explaining to someone how
> they should be voting in approval (beyond "just vote for the candidates you
> like").

In order of complexity:
1) "vote for the candidates you like"
2) "vote for the candidates you like, and don't vote insincerely"
3) "vote for candidates who are above average"
4) "vote for the candidate you would vote for in Plurality, and everyone you
prefer to her"
5) "vote for candidates with a positive strategic value".
6) "vote to maximise the strategic value of your vote".

Me, I'd start at (1) and work my way up to (6), stopping at the point where the
person I'm speaking to seems comfortable with it. If I get to (2) then I should
get better results than Condorcet. If I get to (4) then the strategy should be
"good enough". (5) and (6) are icing on the cake - mathematicians might be
interested, but the extra benefits aren't something to worry about.

> In Ranked Pairs, for instance, it is a simple matter.  Put your
> favourite first, and keep going - stop at any time if you get sick of it.

Of course, that's a nonoptimal strategy: "Put your favourite first, and keep
going, and don't stop" beats it significantly. The complicated offensive
reversal strategies are better yet, but not by terribly much. I'd hazard a guess
that the difference between them and the sincere-lazy-ranking strategy is
equivalent to that between (4) and (6): negligible.

> There is also the potential for mass dissatisfaction from voters who don't
> use the correct strategy, say in a close three way contest where a
> significant chunk of voters have a sincere preference A>B>C, Approval vote
> AB, but an election result where B beats A by a handfull of votes.  If it is
> clear that A would have won in a pairwise contest between the two (and the
> three), Approval voting will become unpopular very quickly,

*shrug* Approval fails the Condorcet criterion. Yep - that's kind of the point:
in order to elect the best SU winner, you have to fail a number of criterion
which people who don't care about SU seem to like. The Condorcet Criterion is
just one of them - the best SU candidate and the Condorcet Winner may well be
seperate people. In this situation the best SU candidate will have a higher SU
than the Condorcet Winner, but will lose to it in a pairwise comparison. If you
think that in this case we should elect the Condorcet winner over the candidate
with the higher SU, then Approval isn't for you, full stop. I'd like to know why
you think that, though.

I think Approval voting will become unpopular as a result with strong A
supporters, and popular as a result with strong B supporters, while weak A and B
supporters will be largely uncaring - people are self-centered like that. There
are likely to be more strong B supporters than strong A supporters, so Approval
should increase in popularity as a result. Condorcet, making the opposite
decision, would decrease in popularity.

> It is much more
> likely in Approval that your vote will be irrelevant, by not expressing a
> preference between the frontrunners.

That's just wrong. Remember, for an instrumental voter, their vote is only
relevant if they break or make a tie. That's it: everything else is irrelevant.
In the case given, those who vote A=B have an irrelevant vote, but those who
vote A>B or B>A have a much *greater* chance of having relevant votes, because
the difference in the vote totals will be correspondingly smaller. On average,
the chance that your vote will be relevant in an Approval election is the same
as in Condorcet. In addition, your vote is more likely to be relevant when you
care about it, and less likely when you don't care about it.

In practice, in almost every large election your vote will be irrelevant from an
instrumental point of view. However, the hugely small probability that it will
be instrumental is the same in Condorcet and Approval.

For non-instrumental voters, their approval vote is always equally relevant,
because its information content is the same no matter what the result of the
election, and these people care about sending a message, not about effecting the


> Approval, more than any other voting system (except probably Cardinal
> Ratings), relies on strategy based on polling results.

Well, and Borda, IRV, and Plurality - who all use strategy based on polling
results to a greater degree than Approval. All of these use burying and reversal
strategies too, which make them more unstable and more vulnerable to

But yes, Approval uses strategy based on polling results (or other means of
playing guess-the-winner) more than Condorcet. I wouldn't say it relies on them
- but if they're there and they're accurate they'll get used to improve the

>  This becomes less true [Condorcet's sincerity] the more complex the election
> gets - say five or ten candidates with a good chance of winning & a
> multi-dimensional issue space meaning an exponential number of voting
> factions / patterns. But this type of situation is even worse for Approval,
> especially if we
> consider the kind of roll polling can play in an Approval election.

Imagine the worst possible case: there are a million candidates with a good
chance of winning, there are as many issues as there are stars in the sky, and
there are rumours that the pollsters have been taken over by three eyed aliens
from Mars.

Everyone concludes that the polls are worthless. The pundits say so. All the
parties say so. The drunk guy down the local pub says so. The media says so. The
three eyed aliens from Mars don't say so, but keep dripping slime into the
microphone. Hey look: we're back in a zero-info election. So the best strategy
is to vote for the parties who are above the average, or simply the candidates
who you like. And a zero-info election will get you a higher SU in Approval than
in Condorcet.

My working goes like this: If you have perfect polls, then Approval beats
Condorcet. If you have diabolical polls with no information content, then
Approval beats Condorcet. It would seem pretty unlikely that somewhere between
these two extremes there is a case where Condorcet beats Approval.

This is exactly the same reasoning as strategy: if you have the perfect
strategy, Approval beats Condorcet. If you have the 0-info strategy, Approval
beats Condorcet. If you have the 'random-sincere-vote' strategy, Approval beats
Condorcet. Assuming that there aren't severe weirdnesses going on, it seems
reasonable to say that Approval beats Condorcet.

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