[EM] What should an ideal single-winner method achieve?

C.Benham cbenham at adam.com.au
Sat Jun 29 05:10:49 PDT 2019

I want to as much as possible give every voter equal positive (from the 
individual voters' perspectives, as far as we can tell from the preferences
they express on their ballots) weight in determining the result. We can 
tend towards "maximising utility" by not encouraging voters to express very
weak (possibly light-minded) preferences or even arbitrary 
not-really-existent preferences that the voting method is unable to 
distinguish from strong
real preferences.

So I'm allergic to any sort of random-fill incentive or a rule common in 
Australia that ballots that don't strictly rank all the candidates have 
no effect on
the result. And I'm not a huge fan of  Later-no-Harm.  Nonetheless IRV 
avoids having any random-fill incentive because it also meets 
Later-no-Help and
so is invulnerable to Burial strategy and that is one of the reasons why 
I rate it as an ok method.

I generally want to reduce insincere strategy incentives, and I want to 
minimise the advantage strategic voters have over sincere voters and the 
that well-informed strategic voters have over less-well informed 
strategic voters. And I prefer that there be no zero-information (about 
how other voters
will likely vote) strategy incentive but if there is it should be 
intuitive and commonsensical.

There is some balance to be struck between guaranteeing the fairest 
result if all the voters are sincere and on the other hand reducing 
strategy incentives
so as to make it more likely that they are, so as to avoid a "garbage 
in, garbage out" scenario.  For that reason some of the methods that 
fail Condorcet
have some justification, because Condorcet is incompatible with 
Later-no-Help (and so has some Burial incentive) and FBC.

Regarding ballot rules, I prefer if the voters are able to express a 
full strict ranking of the candidates if they wish to. It is also nice 
if they can express
above-bottom equal preference and  maybe also an explicit approval 
cutoff or some ratings from which one can be inferred. Some limit on the 
of candidates a voter is allowed to vote above bottom (as with plurality 
and some implementations of IRV I've heard of) is unacceptable.
Approval ballots are also too restrictive.  Three-slot ratings ballots 
are much better but still too restrictive. Four-slot ratings ballots are 
much better again
and might be (at least most of the time) good enough.

Lastly I like to avoid  logical absurdity, such as failures of 
Mono-add-plump and  Irrelevant Ballot Independence and Clone Independence.
BTW, the "strategy incentives" I referred to earlier refer not just to 
voting but also to nomination of candidates.

> Obviously a voting method also needs to be simple enough to understand 
> (in terms of voting and understanding how the winner is calculated)..
If you mean that the voters need to understand how the winner is 
calculated, that view is not universal in the world.

> ... ,and it might be that different types of election suit different 
> methods.
Yes. If the voters trust the people running the election they might put 
up with a complicated voting algorithm they don't understand.  If little 
is at
stake then limiting strategy incentives becomes less important and the 
voters might be content with something relatively simple to save time.

Chris Benham

Toby Pereira tdp201b at yahoo.co.uk
Thu Jun 27 07:31:17 PDT 2019

> With all the discussion of different single-winner methods and the 
> criteria they pass and fail, I'm interested to know what you think the 
> "ideal" method should hope to achieve. For example, some people might 
> want to maximise utility summed across the voters. Others might want 
> to find the candidate that is closest to the "median voter". For 
> others it might be more about obeying some sort of majority criterion 
> (e.g. Condorcet). Etc.
> Personally, the measure that makes most sense to me is to maximise 
> utility. But this doesn't automatically mean score voting (where a 
> score could simply be seen as a utility rating of a candidate), at 
> least in part because strategies that voters adopt might reduce its 
> effectiveness. Obviously a voting method also needs to be simple 
> enough to understand (in terms of voting and understanding how the 
> winner is calculated), and it might be that different types of 
> election suit different methods.
> Toby

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