[EM] STV question (was: re: Hare clustering)

[Colin Champion]

Kristofer - thanks for your reply. Maybe I'm missing something - I'm 
afraid I don't really understand PR. If you have a model of the 
electoral process, you can ask what result it should ideally produce for 
a given set of candidates, but you can also ask what will be the ideal 
result if the candidates are such as allow the voters to express their 
real attributes - their level of class selfishness or sense of social 
justice or greenness or jingoism or whatever. When I read about PR, I 
get the impression that a division into parties is assumed as 
pre-existing, whereas when people talk about single-member voting they 
discuss the effect of the electoral system on the party structure. I 
feel that this latter factor needs to be taken into account.

Suppose that the voters are uniformly distributed over a circular disc 
centred on the origin. Then if a single candidate is elected, he should 
be at O. If there are two seats, the winning candidates can be at 
(-0.4,0) and (+0.4,0). This corresponds to your own 1-D account if the 
parties are left and right, but they could also be up and down.

If there are 3 seats, then the winners should be 120 degrees apart. A 
feature which ties this to single-member elections is that when we 
divide the circle into three 120-degree segments, the ideal candidate 
for each segment is the one whose average distance to voters in the 
segment is least - ie. the ideal single-member winner. I understood your 
original post as partitioning voters into clusters based on their 
rankings of candidates, and then electing one candidate per partition. 
But I understood your partitioning as derived from a given set of 
candidates rather than asking what set of candidates may lead to the 
best result.

If there are 5 seats, perhaps the ideal set of winners is a candidate at 
O and four other candidates 90 degrees apart. When the number of seats 
is large, we pack them like oranges in a crate.

CJC