[EM] Cognitive Dissonance

[Adam Tarr]

David Gamble wrote:

>10% FarRight>Right>Centrist>Left>FarLeft
>10% Right>FarRight>Centrist>Left>FarLeft
>15% Right>Centrist>FarRight>Left>FarLeft
>16% Centrist>Right>Left>FarRight>FarLeft
>15% Centrist>Left>Right>FarLeft>FarRight
>13% Left>Centrist>FarLeft>Right>FarRight
>11% Left>FarLeft>Centrist>Right>FarRight
>10% FarLeft>Left>Centrist>Right>FarRight
>
>I think I've commented on this example before. What would happen if we 
>applied Donald's model to this situation. Firstly, the wing candidates 
>would withdraw/lose support and the situation would become right 35%, 
>centre 31% and left 34 %  ( as Adam predicted I'd say). What would happen 
>then ? There'd probably be a number of deadlocked ballots and either 
>voters would move to the centre or the support for the centre would collapse.
>
>The relative strengths of the centre and the wings are important in a 
>situation like this,
>if the centre is stronger than one of the wings the weak wing's supporters 
>should move to support the centre. If the centre is weak voters will 
>desert it for  the wing candidates. If the centre and both of the wings 
>are of approximately equal strength it is unpredictable what will happen. 
>The short answer is that the election is close and in elections where the 
>results are close a large number of voters are often dissatisfied with the 
>outcome.

OK sure... but which of the following is better:

- roughly one third of the electorate is happy, one third is reasonably 
satisfied, and one third is extremely unhappy, or

- one third is happy, and two thirds is reasonably satisfied?

The answer is obvious, of course.  Basically, to argue that Right should 
win the above example, you have to decide that the second choices of the 
first and eighth factions are more important than the second choices of the 
third and fifth factions.  And there's just no logical reason to do that.

I guess my conclusion here IRV's way of eliminating candidates is, on some 
level, pretty arbitrary.  Sometimes it can work out pretty well, but in an 
example like the one above it clearly drops the wrong candidate.

Now, your objection to Condorcet is that it can allow a centrist to win 
with only a few percent of the first place vote, which, in your mind, is 
just as bad.  I have two responses.  First, this can only happen if that 
candidate can actually rally an overwhelming percentage of the voters to 
give him second place support, which means he can't be all bad.  Having 
pairwise victories over every other candidate IS a significant measure of 
support, second-place votes or not.

Secondly, it's entirely possible for a wing candidate to pull off the same 
trick.  Consider this, perhaps even worse version of my "nightmare 
scenario".  I'll leave out some of the lower preferences that never come 
into play (not exhausting any ballots, just talking out the irrelevant 
parts so it's more readable):

7%  FarRight>Right>LuckyRight>ModerateRight>ModerateLeft
2%  Right>FarRight>LuckyRight>ModerateRight>ModerateLeft
4%  Right>LuckyRight>FarRight>ModerateRight>ModerateLeft
7%  LuckyRight>ModerateRight>Right>ModerateLeft
15% ModerateRight>LuckyRight>ModerateLeft>Right
16% ModerateLeft>ModerateRight>LuckyRight>Left
15% ModerateLeft>Left>ModerateRight>FarLeft>LuckyRight
13% Left>ModerateLeft>FarLeft
11% Left>FarLeft>ModerateLeft
10% FarLeft>Left>ModerateLeft

I called the winner lucky since he got lucky in where he put himself in the 
spectrum.  Really, all I've done here (besides re-name the centrist as a 
left-winger) is splinter my right wing into four candidates.  LuckyRight is 
the second-most moderate, or the third-most conservative.

So now we have a situation where the third most conservative candidate out 
of seven candidates wins, even though that candidate's is in tune with the 
17th percentile voter on the political spectrum.  It's worth noting he only 
has 7% first place support, much lower than the examples you gave below of 
"weak centrists".  What's more, the right wing wins the election with 35% 
of the vote, simply because they got their weaker candidates eliminated 
early on, rather than the left wing which brought two strong candidates 
into the penultimate stage.

>Con         42.8%
>Lib Dem   25.2%
>Lab          28.8%
>Other         3.2%
>
>Assumptions: All Conservative voters express a second preference for the 
>Liberal Democrats, all Labour voters express a second preference for the 
>Liberal Democrats.

Well, you've assumed a centrist party that gets all second-place votes, 
which may or may not be the case.  But at any rate, I think that Condorcet 
is much better suited towards executive positions than use in a 
legislature.  No single-winner method can be expected to produce good 
proportionality.

>Situations in which candidates perceived as being in the centre would win 
>with low first preference votes under Condorcet are much more frequent 
>than situations in which centrists with substantial support would be 
>defeated under IRV ( at least in England in recent history).

Personally, I'd hardly consider 25% to be low first preference 
support.  And as I showed above, IRV does NOT guarantee a strong 
first-place showing from it's winner.  All you need is to be in the right 
position to take advantage of IRV's elimination technique.

-Adam
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