[EM] Cheering for simplicity

[Forest Simmons]

I notice that all of the application that you mention, whether public or
private, seem to assume human candidates and human voters.

Candidate Proxy is sufficient for most such cases, but part of Candidate
Proxy is the Completion Method, which could be a relatively sophisticated
method.

Some of us have interests in which the candidates are sports teams or
alternative courses of action for a robot, for example, and the voters are
the team members or the sports casters or (in the robot case) various
sensors.

Suppose that you are to pick a team of college bowl players from a school
based on their performance on a sample test.

The test questions are the voters. You want a certain kind of
"proportional" representation, not necessarily high scoring players that
answered the same questions correctly.

Here you want to maximize the probability that for a random question at
least one of the players would know the correct answer.

Here the design criteria are different than for a political election with
proportional representation.

In the application at hand, if you had one scholar who could answer 90% of
the questions, and another who could answer only the remaining 10% of the
questions, that would be better than having two scholars who could both
answer only the same 90 percent of the questions.

For political proportional representation it would be better to have two
candidates both approved by the same 90 percent of the voters, than to
have one approved by 90 percent, and the other approved only by the
remaining 10 percent.

This is why some of us are interested in more than just the simplest
methods.

Forest

On Sat, 30 Aug 2003, Dave Ketchum wrote:

> Makes sense for this reflector to serve a variety of interests, but
> identifying interests could simplify understanding for many.  In what
> follows I will concentrate on US public elections:
>        Intellectual reasons - some choose to be here, and some even seem to
> make a buck at it - they confuse the rest of us if they present theory as
> if holding more general interest than it has.
>        Public elections:
>             Executive - for a single winner.  These will continue to exist,
> but we need to get past Plurality, which most of us recognize as not
> deserving to live.
>                  I see this as IMPORTANT, and that Condorcet seems to
> provide a reasonable combination of power and simplicity.
>             PR - for multiple winners for a district.  Many districts are
> designed for a single representative, and may stay that way, using same
> rules as for executive elections.  Some argue for Proportional
> Representation, and debate does not seem yet to produce agreement as to a
> winning method.
>             Non-partisan city elections - New York City, biggest US city
> and bigger than most US states, talks of joining this crowd.  NOT clear
> that they have considered the problems/possibilities, or that EM has
> thought of trying to help.  Of interest, likely 4 Dem candidates and 1
> Rep, based on voter registration and experience with partisan elections -
> seems like Plurality might give Reps more wins than they deserve.
>             US primary elections - another one I hear little of.  I see
> this as a place for Condorcet if topic is single winner.  Note that,
> unlike partisan elections for which we are used to two leading parties,
> candidates may have any possible relation to each other.
>             US presidential elections - a world unto itself.  That each
> state has a quota of members of the Electoral College seems cast in stone,
> but for a state to fill its quota via PR seems worth some thought.
>        Private elections - big deal I notice is that the computers that
> make sense for all public elections may not be appropriate here.
>        What do other countries do - their successes and failures are worth
> noting.
>        Marrying single seat and PR methods?  Tempting but:
>             ONLY if single seat stays Condorcet.
>             PR method must be suitable for that task.
>
> Is Condorcet simple?  I claim YES, especially for the voter:
>        1.  Assign first rank to the candidate you most desire to have win
> (you do not need to consider what chance this candidate may have of
> actually winning).
>        2.  Are there more that you like as well - give them the same rank.
>        3.  Do you want some control of what happens if those you have
> ranked all lose - if so, return to step 1 for the next rank.  Note that
> you only rank so far as you choose - you have ranked one or more as better
> than the remainder, and the remainder as equally below them.
>        This is somewhat like a tournament, with you voting what you see as
> the results of a round.  In counting for each pair of candidates, the
> number of voters who rank the first above the second is compared with the
> number ranking the second above the first.
>             If one candidate wins over each other candidate, that one wins.
>             If two or more candidates tie against each other, but win
> against every other candidate, the tie must get resolved by some means
> such as tossing coins.
>             Else there will be candidates that win over one or more, and
> lose against others.  This is close to a tie, and the counts get compared
> to decide on the winner.
>             Note for candidates you rank as equal - for each pair, if you
> and another voter rank that pair equal, it counts as one win for each
> candidate in the pair.
>
> I read 'Most Condorcet-methods are "brute force" computationally.'  Maybe
> so, but it is not a black mark, for the computation is trivial - certainly
> doable while the next voter is voting, and, for combining results from
> multiple precincts for many candidates, less effort than with IRV - for
> IRV must consider all the voting patterns while Condorcet can work with a
> matrix of totals.  Of course, do a California recall with 135 candidates
> and the time could be significant - but IRV has the challenge of all the
> patterns that could occur with that many candidates.
>
> I read 'but I have heard of the "traveling salesman" problem' - truly a
> champion at eating computer time - but Condorcet and even IRV are not in
> that league.
>
> I read "will always include a Condorcet-winner if one exists" - NOT
> sufficient - for public election we should be unwilling to settle for less
> than picking a winner (unless we have a true tie, or choose to call as a
> tie something close to that).
>
>
> On Fri, 29 Aug 2003 11:09:17 -0700 (PDT) Forest Simmons wrote, per
> subject:  Re: [EM] Cheering for simplicity/Orphan
>
>  > Furthermore, what we call "election methods" have many applications beyond
>  > public elections. We call the alternatives "candidates" because that is a
>  > colorful case that interests a lot of people.
>  >
>  > Forest
>  >
>  > On Thu, 21 Aug 2003, Alex Small wrote:
>  >
>  >
>  >>John B. Hodges said:
>  >>
>  >>>Some time back I asked why the folks here worked so hard to find
>  >>>other methods of Proportional Representation when we had Party List  and
>  >>>STV, which seemed to cover all the necessary bases. People
>  >>>responded with their complaints about both methods.
>  >>>
>  >>Well, many of us are interested in election methods for intellectual
>  >>reasons as well as practical reasons.  Yes, we want to see better election
>  >>methods implemented, but we are also personally intrigued by some of the
>  >>intellectual issues related to election methods.  Devising a different
>  >>election method to satisfy some criterion might help us understand what is
>  >>necessary in order to satisfy that criterion, and hence why certain
>  >>phenomena can occur.
>  >>
>  >>The hope is that some of this can later be used to inform the design of
>  >>simpler election methods, or at least enrich our personal understanding.
>  >>Even if we (hypothetically, mind you, let's not open old debates just now)
>  >>never proposed anything more complicated than Approval and Party List in
>  >>public discussions, a deeper personal understanding would help us when
>  >>questions arise.
>  >>
>  >>Also, there is a small group of professionals who study election methods
>  >>for a living.  In any campaign to introduce a new election method
>  >>(whatever it might be) we will almost certainly butt heads with some of
>  >>them (e.g. Saari).  We need to know what we're talking about.  So an
>  >>academic understanding of the deeper mathematical issues is worth having,
>  >>and proposing arcane methods for fun on this forum may be a good way to
>  >>enhance that understanding.
>  >>
>  >>
>  >>
>  >>Alex
>
> --
> davek at clarityconnect.com  http://www.clarityconnect.com/webpages3/davek
>    Dave Ketchum   108 Halstead Ave, Owego, NY  13827-1708   607-687-5026
>              Do to no one what you would not want done to you.
>                    If you want peace, work for justice.
>
>
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