[EM] Linear Spread Median Range Voting

[rob brown]

I'm not going to try to address each and every point in your long message
(or Yves's) because we are still on completely different wavelengths and I
suspect it would be an exercise in frustration.

Still, I think there is hope.  You seem to understand why median works in
the case of voting for a number.  If you can extend that....but NOT by
simply tacking median onto Range voting, but by fully understanding *why*
median works so well in voting for a number and applying the same concept to
voting on candidates.....maybe you'll see where I am coming from.

Consider the following:

In my example where people are voting on the amount of monthly dues (
http://karmatics.com/voting/moose-example.html ), median works because
people have no incentive to exaggerate.  If the amount that others want is
less than a voter's preferred amount, their vote raises the amount (if the
granularity of nominations is enough, or if it does the sort of
interpolation you suggest), if greater, their vote lowers it.  As you'd
hope.

Exaggerating to try to "swing it as far their way as possible" doesn't help,
and knowledge of how others might vote doesn't give them an advantage.

Now, imagine that instead of voting directly on the dues value, they instead
have several "candidate values" to vote on.  Say the nominated candidates
are:
$7, $8, $9......$25, $26

Now with a Condorcet method (or a DSV method where they rank the candidates
and the system then places an "optimally strategic" approval vote), what do
you know, you'll basically get the same (IMO "correct") result as if people
voted on a number and it did the median thing.  Assuming people were
rational (which, in this case would be both strategic and sincere, since
there would be no conflict), the system would work beautifully and it would
be pretty much identical to the median method.

With your method, even using median on the Range values, not the case at
all.  Anyone who wanted their vote to have the desired effect (as in, move
the result as much closer to their preferred amount as possible) would be in
a position of trying to guess what others were going to vote, and give Range
values appropriately to each "candidate value" so that their vote doesn't
inadvertently move the resulting value in the wrong direction.  (again,
remember that I am talking about the values being voted on, not the Range
values assigned to each nominated value)

BTW, if you want a better means of interpolating for purposes of picking a
median with high granulariy, I can give one to you.  I've done something
similar before.

-r
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