I'll get to the rest later, but:
robert bristow-johnson wrote:
To take an 1D example, the society would be like this:
### ###
##### #####
######################
0-----A----------B-----1
whereas a "centrist" society is like this:
##
######
##################
0-----A----------B-----1
[snip]
If all voters agree about an ideal position (like in the centrist
society above), then there will always be a Condorcet winner. If not,
there may be cycles.
boy, i'd like that explained quantitatively. i am not sure what is
meant by "an ideal position". might you mean that all voters agree
about one of two ideal positions (literally poles, making for a
polarized electorate: "yer either fer W or you be agin' it")? if all
voters agree about a single ideal position, doesn't that make for a
trivial election? like, here in North Korea, we're all for the Dear
Leader.
Okay. What this means is that if the distribution of voters makes up a
function that decays from a central point (like a Gaussian), and this
function has only a single peak (at the central point), and the issue
space is one-dimensional, then there will always be a CW, no matter
where the central point resides with respect to the candidates.
That does not mean that everybody is for Dear Leader. Consider a shifted
example of the "centrist" society above:
##
######
##################
0-------A------------B-1
Now, there will be some people who prefer B to A, but A is still going
to win. The median voter is also closer to A than to B.
It's possible to generalize this to something that Warren calls the
"DDH-median" for multidimensional issue space. See
http://rangevoting.org/BlackSingle.html for a mathematical treatment of
that.
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