Warren Smith ~
If the Condorcet-Kemeny method had been used to calculate the results
for the 135-candidate California special election that was won by Arnold
Schwarzenegger, and even if the voters had used ranked ("1-2-3") ballots
(or range-like ballots that allow assigning three-digit ranking levels),
most of the candidates could be quickly identified as not being a
possible winner. That would reduce the calculations to perhaps as many
as 20 possible-winner candidates. The full ranking -- from most popular
to least popular -- for those 20 candidates could be calculated in
minutes. Yet only the winning candidate needed to be identified, and
there are programming techniques that can quickly identify the winner
without calculating the full ranking results. In other words, the
Condorcet-Kemeny method could identify the winner within a few minutes
(or possibly a few seconds), even if the voters all ranked every one of
the 135 candidates. A few minutes is hardly a lifetime (although there
may be times when it might seem like it is).
You refer to randomly generated ballot preferences, which takes your
argument out of the realm of normal elections. Yet there is a real-life
situation that is similar to randomly generated ballot preferences.
Imagine a survey or poll that is ranking a "top 100" list of musical
songs, putting them in sequence from most popular down to least popular.
For this purpose there is a variation of the Condorcet-Kemeny method I
would recommend, and it would easily handle such extreme cases (and then
the top 20 songs could be more precisely ranked using the full
Condorcet-Kemeny method). I have not yet publicly described this
alternative, but I intend to later, when I have more time.
Presumably your reason for attempting to find weaknesses in the
Condorcet-Kemeny method is that it's fairness of always identifying a
Condorcet winner in combination with the fact that it is relatively easy
to explain (certainly much easier to explain and understand than the
Condorcet-Schulze method -- which is a consideration I pointed out to
you yesterday during our declaration-editing chat) makes it seem
uncomfortably competitive with your preferred election method, which I
believe is Range voting. If I have interpreted correctly, thank you for
this compliment of the Condorcet-Kemeny method.
By the way, if a real election is likely to involve 20, or 50, or more
choices, then I recommend using VoteFair Ranking as described in my
book, "Ending the Hidden Unfairness in U.S. Elections". VoteFair
Ranking uses "VoteFair party ranking" to identify which political
parties deserve to have two candidates in the main election, and which
parties are not popular enough to justify having any candidates. This
limitation is not for the purpose of reducing calculation time, but
rather for the purpose of giving voters a reasonable number of
candidates to keep track of, without distractions from
cannot-possibly-win candidates.
Richard Fobes
On 9/11/2011 9:22 PM, Warren Smith wrote:
I have on this thread at the CES
http://groups.google.com/group/electionscience/t/b135bdc214c39ffa
reviewed some known theoretical and empirical facts about the Kemeny Condorcet
voting method.
In particular, it appears based on my literature review that humanity,
using 2006-2011 era hardware and software, is currently unable to
reliably determine the Kemeny winner from the votes in 5-voter,
50-candidate test elections generated by certain reasonable kinds of
random vote-generating processes.
The Wikipedia article
http://en.wikipedia.org/wiki/Kemeny%E2%80%93Young_method
is somewhat misleadingly worded on this point. It makes it sound
like no problem,
but actually the very paper they cite says quite the opposite.
Further comments will be welcome.
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