[EM] Cognitive Dissonance

[Dgamble997]

Adam Tarr wrote in response to the realism of Eric Gorr's example being evaluated:

"Oh, that's the problem. Great. Now that that's cleared up, let's make a
realistic example:

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

Now explain why this is unrealistic. Here, I'll help you out: you're going
to ignore the first preferences of the most extreme fashions, and magically
turn this into a three way race, at chich point your standard
anti-weak-center logic will apply. Or, you're just going to ignore
me. That's worked in the past...

It takes a good dose of cognitive dissonance to argue that the above
example should result in someone other than Centrist being elected."

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.

I recently examined the results of the 2001 British general election for English seats to look for patterns of voting that would lead to the following situations:

Victory for centrist with low first preference vote ( less than 20%) under Condorcet:

108 seats out of 529

Typical example seat

Basingstoke

Con         42.7%
Lib Dem   13.9%
Lab          40.9%
other        2.5%


Defeat for centrist with substantial 1st preference support (25% or more) under IRV

Liberal Democrat has 25%+ of the 1st preference vote but would be eliminated under IRV as a result of coming third.

7 seats out of 529

Typical seat

Bournemouth West

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.

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).

David Gamble