[EM] Can every issue be resolved on to a 1D spectrum?

[James Green-Armytage]

Gervase Lam wrote:
>What if a candidate said that capital punishment would be meted out on
>the 
>first offence but then life imprisonment on the second?  What I am trying 
>to think of in this case is a discontinuous bolt on to the 1D spectrum.

I reply:
	Yes, I understand. I agree that very few issues can be reduced to a 1D
spectrum without some sort of artificial simplification. If you are simply
discussing the number of months in prison that should be imposed in
punishment for a single offense, then you are relatively close to a 1D
spectrum. However, if you throw in other kinds of punishments, then you
have to make some sort of judgement as to where they fit in on the
spectrum, a judgement that perhaps not everyone will agree with. Thus, a
cycle is possible even in the sincere preferences of the electorate.
	1D spectrums are very nice things to deal with from a voting methods
theory point of view because when there is a guarantee that options lie
along a 1D spectrum, it is possible to do away with strategic incentive
altogether (by forcing people to arrange their preferences consistently
with the spectrum). However, situations where such a limitation would be
accepted may be rare.
	When Condorcet is applied to a 1D spectrum and people vote sincerely, the
median option will always be chosen. This is a good argument for
Condorcet's method. Widespread use of strategy can muddy the waters,
though.
	If you have a non-binding direct democracy system based on pairwise
comparison, which is what I have proposed, results of public votes are
subject to further interpretation by lawmakers. Thus, if there is no
Condorcet winner in the result but lawmakers are convinced that the issue
is close to being a 1D spectrum, they should be able to determine the
median result without too much difficulty. This further decreases the
incentive for strategy in the vote.
	Although true 1D spectrums may be rare in public voting, if an issue is
close enough to a 1D spectrum, voting on that issue should be relatively
straightforward, as there should be an approximated 'median area' where
the winning option is located.
	I think that the important thing to come to a consensus on now is that
when there is an issue that is close enough to a 1D spectrum, that a
choice that is close to median is highly preferable.

James