[EM] Weak Condorcet winners

[James Gilmour]

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.


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


> (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.

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.


> 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.
 

> > 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.

James Gilmour