[EM] Weak Condorcet winners

[Juho Laatu]

On 23.9.2011, at 16.31, James Gilmour wrote:

> Juho  > Sent: Friday, September 23, 2011 12:29 PM
>> I think term "weak CW" should not be used as a general term 
>> without referring to in what sense that winner is weak. There 
>> are different elections and different needs. In some of them 
>> weak CW is a good choice, in some others not.
>> 
>> 51: A
>> 49: B
> 
> Yes, this CW is weak in terms of difference from the opposition, but that weak winner will be accepted by the electorate who, in
> countries like the UK, USA and Canada, take a majoritarian view.  And it will be accepted by the partisan politicians because "next
> time, it could be our turn".
> 
> 
>> As you can see A is a weak CW here. Not so if you measure the 
>> number of first preferences, but very much so if you compare 
>> the strength of the winner to the strength of its competitors.
>> 
>> 45: A>B>C
>> 5: B>A>C
>> 5: B>C>A
>> 45: C>B>A
> 
> If this is an election, I don't think the Condorcet winner here, with only 10% of the first preferences, would be effective in
> office in a country with an electorate of majoritarian view and partisan politicians and media to match.

Depends on what kind of office we are talking about. If we want the winner to ideally have a majority we still have at least two viewpoints. We might want the winner to have majority of first preferences, or we might want the winner to beat all others with majority. In two-party countries I can understand that the winner should be either A or C (the representatives of the two parties). But already in multi-party countries the idea that one should always elect from the big parties, even if we have a compromise candidate that is preferred to the big party candidates, is not as strong. And if we think about offices where the candidates are not linked to any parties (meaning that only the personal characteristics of the candidates are important), we might want the CW to win always.

Note also that in a two-party country we might have an election with opinions 40 A>B>C, 11 B>A>C, 49 C>B>A. A and B come from the same party. We want the winner to be B. B has as much strong support from his own party as A would have, in the sense that they have the full party machinery working for them once elected. The requirement of strong first preference support thus assumes also that we already had preliminaries where the representatives of the two parties (or all separate parties) were nominated, and therefore the method can trust that a "weak CW" never comes from a major party. (Since otherwise we would have to elect a "(technically) weak CW" because he is not a "(politically) weak CW" after all.)

> 
> 
> But now you have introduced something completely different.  This next example is an exercise in choosing among policy options.  
>> A = set tax level to 20%
>> B = set tax level to 19%
>> C = set tax level to 18%
>> 
>> It is obvious that B is the alternative that should be 
>> chosen. Other end results would be plain wrong. B is not a 
>> weak candidate in any way.
> 
> Your are wrong to use the word "candidate" here.

Yes, normally I use word "alternative" when I don't want to specify whether the alternatives are humans, policies, ice cream flavours or something else.

>  This is not a candidate election  -  it is a decision about policy options.  And
> that is something very different.

Yes, but the scale is quite continuous. The non-party-bound official example that I gave above was quite close to this policy example. Human candidate elections that require strong first preference support are one special case.

>  In my experience, the attitudes and approaches of electors (and even politicians) to these two
> different tasks also differ.  What would be acceptable in making a policy decision (a weak Condorcet winner) would not be acceptable
> in a candidate election.

Often so. Depends on what kind of candidate election and in what country we are talking about.

>  This is a practical distinction the advocates of a social choice approach (sociology + political economy)
> have failed to understand and appreciate.
> 
> 
>> Term "weak CW" seems to be heavily linked to the 
>> understanding that the winner should have lots of first 
>> preference support
> 
> This is what electors, at least in some countries (UK, USA?, Canada?) clearly seem to be wanting and saying.

Yes, that is in their blood, that is what they are used to.

>  As I said in first
> post under the original heading, I think we could sell the third-placed Condorcet winner provided that candidate was not too far
> behind the front two in first preferences.  But the really weak CW, that is weak in first preference votes (5% or 10%), is not worth
> thinking about in terms of practical reform of the voting system to be used for public elections in such countries.

Yes, I can understand that. And particularly, if we would use this Condorcet method to pick winners in singe-seat districts of a two-party country, we could end up destroying that kind of "two-party proportionality" that we are used to, when using FPTP. In that kind of a system the whole idea is to give all (or almost all) seats to two (or maybe three or four) major parties.

> 
> 
>> (or it should often belong to the most 
>> preferred subgroup of the candidates). This is a viewpoint 
>> that is quite strong in two-party countries (that want to 
>> stay as two-party countries) since in those countries whoever 
>> is in charge has typically more than 50% support among the 
>> voters.
> 
> No, that is typical only of the USA (a very atypical example of FPTP)  -  it is not typical of the UK or Canada.  NO government in
> the UK since 1945 has been elected with even 50% of the votes, never mind "more than 50% support among the voters".  But with two
> exceptions, all of those governments had absolute majorities of seats in the Parliament.

Yes, true, just picking the strongest party here, not necessarily a party with over 50% support.

> 
> I am not sure how you define "two-party countries", but for several decades the UK has had three significant parties and Scotland
> and Wales have each had four significant parties.  And the majoritarian view of single-winner elections prevails.

I believe I use that pretty often as a synonym for countries that use single-winner district based methods to elect representative bodies. Not accurate - I know.

> 
> 
>> But what is weak in this kind of thinking need not be 
>> weak in some other set-up.
> 
> But what matters here is the perception of the electors  -  and how the partisan politicians (and hostile media) could exploit that
> to render a weak Condorcet winner ineffective in office.

Yes, and I might agree that Condorcet is not the best method for all single-winner needs.

> 
> 
>>> Failing the majority criterion is, in my view, a similar flaw to 
>>> electing a weak CW.
>> 
>> I think electing a weak CW is a flaw only in some set-ups 
>> with some specific requirements that make weak CW a bad 
>> choice. Majority criterion is a requirement far more often, 
>> but not always. There are also elections where majority is 
>> not a requirement. And there are also elections where it is 
>> sometimes a requirement to elect against the majority opinion.
> 
> This sounds more like (benign) dictatorship than democratic representation.

I thought about some non-competitive elections. We might use e.g. range to elect the pizza that we will share.

2: A=99, B=100
1: A=100, B=0 (this person is allergic to some ingredients of pizza B)

Pizza A is obviously the best choice although a clear majority of the voters prefer pizza B.

Juho



> 
> James Gilmour
> 
> 
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