[EM] CR style ballots for Ranked Preferences

[Anthony Simmons]

>> From: Jobst Heitzig <heitzig at mbox.math.uni-hannover.de>
>> Subject: Re: [EM] CR style ballots for Ranked Preferences

> >> However, what I can't see is why this should be of any
> >> importance. Instead, it just shows that in order to
> >> determine the winner, one cannot divide the electorate
> >> into groups but must consider all voters simultaneously!

>> I would like to emphasize this again: In order to use a
>> rule that has this presumably negative property of
>> "inconsistency", one only must assure that the whole
>> electorate is treated simultaneously. For summable rules,
>> there is no problem in doing so!

But isn't summability the whole basis of an election?  We
have a lot of preferences on the smallest scale (the
individual), and wish to somehow combine these to formulate a
preference on the largest scale that accurately summarizes
the individual preferences.  There's something strangely
suspicious about a process that supposedly does this but
gives different results at an intermediate scale.  We have to
wonder whether it is the intermediate or largest scale that
is not accurately summarizing the preferences of the voters.

We expect that the social choice will be an accurate summary,
in some fashion, of individual choices.  That is, it's not
just a bunch of rules, an arbitrary function, but a measuring
device that tells us something empirical about the world.

Suppose we wish to measure the color of a section of a
mosaic.  Looking at the section as a whole, our measuring
device tells us that the section is white, but if we point it
at individual tiles, the same device tells us they are black.
We might conclude that the device is giving us an inaccurate
reading on one of the scales, but which one?

Likewise, if the device we use to measure the public will
gives different readings on different scales, we conclude
that it is giving faulty readings on one of the scales, but
which is it?

>> > We have an interesting institution in the U.S., which
>> > illustrates the importance of arbitrary boundaries:  The
>> > electoral college.  California gets a certain number of
>> > electors in the presidential election.  If, as some people
>> > would like, California were to split into two states, the
>> > total number of electors for California would be increased by
>> > two.  Same people, same territory, two more electors.

>> Right - okay. But doesn't that show that this voting
>> system is quite bad?  ...

Yes, calling it "quite bad" is a good way to put it.

>> ... Anyway, I don't think the notion of
>> "inconsistency" applies also to voting systems that elect
>> representatives instead of a single winner. How would
>> "inconsistent" be defined then? What I was talking about
>> was the situation where the electorate elects one winner,
>> and I still cannot see why this decision should take place
>> first in groups rather than at once.

The system I was talking about is the one we use to choose
our President.

It gives an interesting perspective.  The original plan was
that each state would vote, with some states getting more
votes than others.

>> Jobst