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Hi,<br>
<br>
[I'm not subscribed to <a class="moz-txt-link-abbreviated" href="mailto:RangeVoting@yahoogroups.com">RangeVoting@yahoogroups.com</a>, so I won't see
replies posted only there.]<br>
<br>
On 1/9/09 Dave Ketchum wrote:
<blockquote cite="mid:49678921.8090503@clarityconnect.com" type="cite">Extended
now to EM - I should have started this in both.
<br>
On Fri, 09 Jan 2009 15:40:58 -0000 Bruce R. Gilson wrote:
<br>
<blockquote type="cite">--- In <a class="moz-txt-link-abbreviated" href="mailto:RangeVoting@yahoogroups.com">RangeVoting@yahoogroups.com</a>, Dave
Ketchum <a class="moz-txt-link-rfc2396E" href="mailto:davek@..."><davek@...></a> wrote:
<br>
<blockquote type="cite">We need to sort thru the possibilities of
going with Condorcet. I claim:
<br>
<br>
Method must be open - starting with the N*N matrix being available to
anyone who wants to check and review in detail.
<br>
<br>
If the matrix shows a CW, that CW better get to win.
<br>
<br>
Cycle resolution also better be simple to do. We need to debate what
we document and do here such as basing our work on margins or vote
counts.
<br>
</blockquote>
<br>
Yes. My biggest gripe with Condorcet is that cycle resolution in many
systems is so complex that it does not seem that a typical voter (as
opposed to people like us who are personally interested in electoral
systems) could understand what is being done. <br>
</blockquote>
</blockquote>
-snip-<br>
<br>
I think there's no need to gripe or fret. Resolving cycles doesn't
need to be complex. Here are 2 solutions.<br>
<br>
1) The "Maximize Affirmed Majorities" voting method (MAM) is an
excellent Condorcet method and is very natural. Here's a simple way to
explain how it works and why:<br>
<br>
<big><font size="2"><big>The basis of</big></font><font size="2"><big>
</big></font><font size="2"><big>the
majority rule principle is that the more people
there<br>
are who think candidate A is better than candidate B, the more
likely <br>
it is</big></font><font size="2"><big> that A will be better than
B for society. (Regardless of whether <br>
they think A is best.) <br>
<br>
Since majorities
can conflict like "rock paper scissors" (as shown in the<br>
example that follows) the majority rule principle suggests</big></font><font
size="2"><big> such conflicts <br>
should be resolved in favor of the larger majorities.
<br>
<br>
Example: Suppose there are 3 candidates: Rock, Paper and Scissors.
<br>
Suppose there are 9 voters, who each rank the candidates from best
<br>
to worst (top to bottom):</big></font><font size="2"><big> </big></font><font
size="2"><big><br>
</big></font></big><big><br>
<b><tt> <font size="2"><big><u>4</u></big></font><font size="2"><big>
</big></font><font size="2"><big><u>3</u></big></font><font
size="2"><big> </big></font><font size="2"><big><u>2</u></big></font>
<br>
</tt><tt><font size="2"><big>Rock Scissors
Paper</big></font>
<br>
</tt><tt><font size="2"><big>Scissors Paper
Rock</big></font>
<br>
</tt><tt><font size="2"><big>Paper Rock
Scissors</big></font></tt></b></big><b><tt>
</tt><br>
</b><big><tt><br>
</tt><font size="2"><big> 7 voters (a majority) rank Scissors over
Paper.<br>
6 </big></font><font size="2"><big>voters (a
majority) rank Rock over Scissors.<br>
5 voters (a majority) rank </big></font><font size="2"><big>Paper
over Rock. <br>
<br>
</big></font><font size="2"><big> By paying attention first to the
larger majorities--</big></font><font size="2"><big>Scissors
over Paper, <br>
then Rock over Scissors--we establish that</big></font>
</big><big><font size="2"><big>Scissors finishes over Paper<br>
and </big></font></big><big><font size="2"><big>then that Rock
finishes over Scissors:<br>
<br>
</big></font></big><big><b><tt> </tt><tt><font size="2"><big>Rock
</big></font><br>
</tt><tt><font size="2"><big>Scissors</big></font><br>
</tt><tt><font size="2"><big>Paper</big></font></tt></b></big><b><br>
</b><big><tt><br>
</tt></big><big><font size="2"><big></big></font><font size="2"><big>
It can be seen at a glance that Rock also finishes over Paper. <br>
T</big></font><font size="2"><big>he
smaller majority who rank Paper over Rock are outweighed</big></font><font
size="2"><big>.<br>
<br>
Since Rock finishes over both Scissors and Paper, we elect Rock.</big></font><br>
<br>
</big>I think that's not too complex. (How did anyone reach the
dubious conclusion that beatpaths or clone-proof Schwarz sequential
dropping will be easier than MAM to explain?) I think the only
operational concept that will take work to explain is that there is
more than one majority
when there are more than two
alternatives. (Analogous to a round robin tournament, common to all
Condorcet methods, and not really hard to
explain.) Most people already know what an order of finish is, and I
think
most people are familiar enough with orderings that they will recognize
the
transitive property of orderings when it's presented visually.<br>
<br>
Jargon terms such as "Condorcet winner," "beats pairwise" and "winning
votes" are unnecessary. Their use may interfere with moving ahead.<br>
<br>
Top-to-bottom orderings are more intuitive than the left-to-right
orientation many other writers use in their examples. Two common
meanings of "top" are "best" and "favorite." Two common meanings of
"bottom" are "worst" and "least favored." In those contexts, "over"
means "better" or "more preferred." Left-to-right offers no such
friendly connotations (except to the "leftist" minority, and the
opposite to the "rightist" minority). Left-to-right becomes even worse
when symbols like the "greater than" sign
(>) are used, since a lot of people are repelled by math symbols.
Left-to-right rankings may interfere with moving ahead.<br>
<br>
2) One could promote the variation of Instant Runoff (IRV) that allows
candidates to withdraw from contention after the votes are published.
(I'm not suggesting eliminating the secret ballot. The corresponding
voters' identities would not be published.) The withdrawal option
mitigates the spoiling problem of plain IRV. It reduces incentives for
voters to misrepresent preferences (true also for Condorcet methods,
but I think not true for Range Voting, Approval or Borda). I expect
IRV+Withdrawal would exhibit a solid Condorcetian tendency to elect
within the sincere top cycle, since supporters of spoilers would
pressure them to withdraw when needed to defeat their "greater evil."
Obviously, its promotion could leverage the efforts of the promoters of
plain IRV. It can even be argued that IRV+Withdrawal satisfies the
spirit of the Later No Harm criterion, if people (or courts) care about
that.<br>
<br>
Assuming IRV+Withdrawal were employed by society for many elections,
the eventual switch to a Condorcet method like MAM (or MAM+Withdrawal)
would either be found to be unnecessary, or would become fairly obvious
due to observations of candidates' occasionally ignoring their
supporters' pressure to withdraw (or to not withdraw).<br>
<br>
Best wishes,<br>
Steve<br>
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