[EM] No evidence that IRV doesn't fail. Reasons why it must.

[Paul Kislanko]

>Eric asked:
>> Why do you believe that the first place preferences matter more then
>> the middle or final preferences? What is the basis for this
>> assumption?

James answered:

>Unless you ask the voters specifically you cannot know, but I think there
is an intuitive answer.
>Consider a Borda election in which a candidate, with a majority of the
first preference votes is
>defeated.  I think most voters would intuitively consider such a result to
be "wrong".  Those
>immersed in social choice theory may argue that such voters have been
brainwashed by decades of
>exposure to plurality voting systems and need to be educated to see the one
true light.  But I know
>from experience what the intuitive reaction of most voters is.  On that
basis I think we can say
>that first place preferences do matter more than later preferences.  But
that, of course, is quite
>different from constructing a voting system that depends on assigning
specific values to successive
>preferences when you have not asked the voters what those values might be.

There's more than "intuition" on the side of the relative importance of
different positions in relative rankings. In general it is much easier for
most of us to decide the relative ranking of 1st and 2nd choice than 4th and
5th. There's no doubt a lot of references to cognitive research on this
subject, but "intuitively" you can try it on yourself with ice cream
flavors - I love Butter Pecan, but not too much more than Peaches 'n Cream,
and both of those are down on the list somewhere. When presented with a list
of, say 31 flavors, I can agonize over having to choose between 2 or 3 and
won't waste time on anything below some top 'n' - and I usually choose one
scoop each of my top 3...

Where I disagree a bit with James  is that I think it is too much to ask the
voters to quantify their subjective rankings by coming up with their own
weights. By the time I get to 4th and 5th, it is hard enough to distinguish
which should be 4th, much less assign some value to the "by how much"
function. In theory the voter is the only one who knows, but the voter will
have to solve a math problem to figure out what numbers to put in, and
most - even including us math majors - won't really want to do that when our
brains should be deciding who to elect to govern us instead of mentally
solving some equation. Even if we did, we'd all do it a different way, and
you'd come up one with voter's third choice being given more weight than
another voter's third choice, unless you take some exceptional measures to
manipulate the individuals "rating" (without the voter knowing).

So, I would say that the "utility" or "cardinal rating" of an Nth-place
ranking should be the same for all voters and known to all voters, which
would make it a function of the number of alternatives. If the function is
linear, it is just a disguised form of Borda counts, but as the ice cream
example shows it most definitely should not be linear.