[EM] Re: Empirical data on cycles

Jobst Heitzig heitzig-j at web.de
Sun Sep 4 04:46:34 PDT 2005

Dear Rob!

>From the following natural example, it seems to me DMC and wv are more
truncation resistant than margins:

  46 A>C>>B
  05 C
  49 B>C>>A
C is Condorcet Winner.

  46 A>C>>B
  05 C
  49 B
C still wins in DMC and wv, but B wins in margins.

Furthermore, also Smith//Approval has a problem here: Although it still
elects C here, only 3 of the A voters need to forget to approve of C to
make B the winner:

Truncation and Lazyness:
  03 A>>C>B
  43 A>C>>B
  05 C
  49 B
C still wins in DMC and wv, but B wins in margins and Smith//Approval.

What do you think?

Yours, Jobst

Rob LeGrand wrote:

> Adam Tarr wrote:
>>It suggests to me that _natural_ cycles are very rare. This does
>>not automatically mean that cycles can never be a problem. The
>>important thing is to pick a Condorcet method where, when a
>>Condorcet winner exists in sincere preference, it is extremely
>>rare than any faction has a tactic where they can cause a
>>favorable cycle. (I am referring, of course, to winning votes.)
> Any such cycle-creating strategy that exists under a margins method
> also exists under the equivalent winning-votes method.  If the
> margins strategy includes no equal ranking, the strategies are the
> same.  If it includes equal ranking, such as changing sincere
> 20:A>B>C>D
> ballots to
> 20:A=B>D>C
> ballots, an equally successful winning-votes strategy would be
> 10:A>B>D>C
> 10:B>A>D>C
> So such situations are no rarer under winning-votes than under
> margins.  If anything, it seems to me that winning-votes might
> provide more such opportunities to the strategic voter since equal
> ranking has no effective equivalent under margins.  (But it's
> usually more effective just to order-reverse anyway.)  It is for
> this reason and the fact that winning-votes encourages equal ranks
> near the top of the ballot and full ranking near the bottom even
> when insincere (and even in the zero-info case!) that I prefer
> margins to winning-votes.
> --
> Rob LeGrand, psephologist
> rob at approvalvoting.org
> Citizens for Approval Voting
> http://www.approvalvoting.org/
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