Re: Fw: Voting project

From: David Mertz <voting-project_at_gnosis_dot_cx>
Date: Mon Aug 11 2003 - 15:17:33 CDT

|> I'm completely ignorant about "Instant Run Off Ballots"...

|The basic idea of IRV (or "choice voting" or "ranked preference voting") is
|that if no candidate gets a majority, candidates can pick up additional
|votes depending on how many times voters had them as their 2nd place, 3rd
|place etc. choice. This eliminates the spoiler role, although it also
|changes the complexion of voting in other ways.

To elaborate slightly. IRV lets voters pick an ordered list of
candidates. The tabulation goes through several rounds of calculation,
until one candidate gets a majority.

In the first round, every voter's #1 pick is examined. Each candidate
gets a certain percentage, but in many-candidate races, quite likely no
one candidate gets >50%. Assuming there is no majority candidate,
tabulation goes to a second round.

In the second round, the least popular candidate, "Smith," from round one
is simply eliminated. All the voter who picked Smith as #1 have all
their rankings moved up a notch. I.e. #2 becomes #1 (and #3->#2, etc)
for that voter. Even voters who picked Jones in a different position
have the votes below Smith adjusted too, btw. Using this new set of #1
rankings, we check again whether anyone has a majority.

If necessary, keep going through rounds until there are only two
candidates left on ballots. At this point, one or the other must have a
majority (well, it could be an exact tie, but that's unlikely for a
large vote--more than a local club).

The goal of the IRV style is to let voters cast a vote for who they
REALLY want, without feeling like they're "throwing away their vote"
(when they could vote for the "lesser of evils"). For example, in the
2000 USAian Presidential race, the Green party fielded a candidate,
Nader. The large majority of voters who really preferred the Greens
thought that Gore (Democrat) was a lesser evil than Bush (Republican).
So a certain share of "natural Green" voters voted for Gore, since they
only had one single preference to express as USAian ballots are set up.
And all those Greens who *did* vote for Nader lost any way of expressing
their relative preference for Gore over Bush.

However, all styles of tabulation (by mathematical proof--not given
here, but it exists) produce results that are intuitively "wrong" in
some cases, IRV included. For example, suppose you have these ballots:

       A B C D E
  +----------+ +----------+ +----------+ +----------+ +----------+
  | Jones | | Wu | | Hassam | | Jones | | Wu |
  | Martinez | | Martinez | | Martinez | | Martinez | | Martinez |
  | Hassam | | Hassam | | Wu | | Hassam | | Hassam |
  | Wu | | Jones | | Jones | | Wu | | Jones |
  +----------+ +----------+ +----------+ +----------+ +----------+

In this case, Martinez is eliminated in the first round of tabulation...
even though she is *everyone's* second choice (i.e. no one really
-dislikes- Martinez). The second round looks like:

       A B C D E
  +----------+ +----------+ +----------+ +----------+ +----------+
  | Jones | | Wu | | Hassam | | Jones | | Wu |
  | Wu | | Hassam | | Wu | | Hassam | | Hassam |
  | Hassam | | Jones | | Jones | | Wu | | Jones |
  +----------+ +----------+ +----------+ +----------+ +----------+

Now Hassam has the fewest #1 rankings, so let's eliminate him for the
next round.

       A B C D E
  +----------+ +----------+ +----------+ +----------+ +----------+
  | Jones | | Wu | | Wu | | Jones | | Wu |
  | Wu | | Jones | | Jones | | Wu | | Jones |
  +----------+ +----------+ +----------+ +----------+ +----------+

So Wu wins. Still, in the first round 3/5 of the voters preferred
Martinez to Wu. And 2/5 of the voters actively disliked Wu enough to
rank her last (nobody ranked Hassam last either).

But every other systems has its own paradoxes. You could let the ranks
stand for points, for example. Say, first choice gets 5 points, second
4, etc. Then you add the points to decide the winner. You can
construct cases where the outcome seems wrong according to this rule
also.

Yours, David...

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Received on Sun Aug 31 23:17:08 2003

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