[EM] Re: Election-methods Digest, Vol 8, Issue 4
William Redpath
wredpath at his.com
Wed Feb 2 12:37:25 PST 2005
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Subject: Election-methods Digest, Vol 8, Issue 4
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> Today's Topics:
>
> 1. Re: simulating an Approval campaign/election (Rob LeGrand)
> 2. Comparative Effectiveness of Approval and Condorcet in the
> case of a three candidate cycle. (Forest Simmons)
> 3. apology for "no subject" posting (Forest Simmons)
>
>
> ----------------------------------------------------------------------
>
> Message: 1
> Date: Tue, 1 Feb 2005 16:06:44 -0800 (PST)
> From: Rob LeGrand <honky1998 at yahoo.com>
> Subject: [EM] Re: simulating an Approval campaign/election
> To: Election Methods Mailing List <election-methods at electorama.com>
> Message-ID: <20050202000645.20547.qmail at web30405.mail.mud.yahoo.com>
> Content-Type: text/plain; charset=us-ascii
>
> Russ wrote:
>> Interesting. Do you mind if I ask why you are interested in
>> Declared-Strategy Voting as opposed to Undeclared-Strategy
>> Voting?
>
> DSV is the invention of Lorrie Cranor and the subject of her
> dissertation (http://lorrie.cranor.org/dsv.html). "Declared" just
> means that a voter declares a strategy for the DSV system to use to
> vote for him in the simulated election(s).
>
>> Does another strategy converge even if no Condorcet winner
>> exists?
>
> In the example
>
> A B C
> 9: 100 0 90 (9 voters have utility 100 for A, etc.)
> 8: 90 100 0
> 6: 0 10 100
>
> the only equilibrium when all voters use strategy T is
>
> 9:A
> 8:B
> 6:CB
>
> The same is true for strategies B (Poll Assumption (Approval) from
> 7.4 of Brams and Fishburn's Approval Voting) and I (change the
> approvals from your last ballot just enough so that you approve of
> one of the two frontrunners and not the other). Note that the
> equilibrium disappears if the 9 A-favorite voters realize that they
> can improve the outcome from their perspective by approving C in
> addition to A, as strategy A would recommend.
>
>> I assume you mean that plurality can be manipulated by throwing
>> in spoilers (e.g., Nader or Perot).
>
> No, I mean that when everyone votes strategically (giving "spoiler"
> candidates no votes), those that are voting insincerely are
> manipulating the election, usually into equilibria that allow
> little chance for candidates that might turn out to be Condorcet
> winners. Not that there's anything wrong with this manipulation--
> it's the smart way to vote if you want to affect the outcome.
>
>> And as for multiple equilibria, it seems to me that all but one
>> of those equilibria is practically inaccessable if it requires a
>> third party to switch places with one of the two dominant
>> parties.
>
> I agree that plurality leads to a static two-party structure.
> Other systems that lead to equilibria more often than Approval also
> lead to party systems that limit entrance of new candidates and
> parties. Approval is the most stable voting system I know that
> still allows a dynamic (and party-less?) political system; at the
> extremes, plurality gives you stability at the expense of openness
> and Borda gives you dynamism (too much!) at the expense of ultra-
> instability. Also, plurality encourages each ideology to run at
> most one candidate (and often none), Borda encourages each ideology
> to run many candidates, and Approval encourages running those
> candidates that have a chance to win.
>
>> You seem to have confirmed my hypothesis that, in the idealized
>> case (DSV batch mode), Approval voting almost always converges on
>> the Cordorcet winner if one exists, but rarely (never?) converges
>> if one does not exist.
>
> Yes, that's true, if all voters use strategy A or something very
> much like it, which according to my investigations is in their best
> interest.
>
>> If that is true, then it seems to me that Approval may be roughly
>> equivalent to Condorcet with random selection of the winner from
>> the Smith set. Do you agree with that?
>
> Only very roughly. The selection from the Smith set is random
> (assuming that the number of rounds is large and at least
> pseudorandom, e.g. based on the number of voters in a large
> election in a way that makes it very difficult to predict), but
> some members of the Smith set may have no chance of winning.
>
>> If so, has anyone shown that the Condorcet winner based on a
>> "good" Condorcet resolution method would at least be favored in
>> the random selection process?
>
> That depends on the random selection process. If you use regular
> batch DSV and stop after a predetermined number of rounds, you'll
> get different winning probabilities than if you use cumulative
> batch mode or ballot-by-ballot mode. According to my simulations,
> the above example election run in ballot-by-ballot mode for a large
> random number of rounds would give A, B and C win probabilities of
> approximately 45.8%, 32.0% and 22.2%. Most of us would agree that
> A has the best claim to victory, followed by B. Batch mode gives A
> 50%, B 25% and C 25% (tight loop); cumulative batch mode gives
> roughly A 30.4%, B 47.8% and C 21.7%. (The win probabilities for
> cumulative batch mode are relatively difficult to measure because
> the intervals between leader changes become longer and longer as
> the number of rounds increases.) To me, these results confirm my
> intuition that ballot-by-ballot (with a random voter order in each
> round) is a fairer way to find a winner than the batch modes given
> a large number of rounds.
>
> =====
> Rob LeGrand, psephologist
> rob at approvalvoting.org
> Citizens for Approval Voting
> http://www.approvalvoting.org/
>
>
>
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>
> ------------------------------
>
> Message: 2
> Date: Tue, 1 Feb 2005 17:19:48 -0800 (PST)
> From: Forest Simmons <simmonfo at up.edu>
> Subject: [EM] Comparative Effectiveness of Approval and Condorcet in
> the case of a three candidate cycle.
> To: election-methods-electorama.com at electorama.com
> Message-ID: <Pine.LNX.4.61.0502011538480.11856 at lhotse.up.edu>
> Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed
>
> Russ brought up the issue of effectiveness of Approval.
>
> I think that we are mostly in agreement now that Approval locks on to the
> CW fairly quickly when there is a CW. "Quickly" can even mean during the
> first election if DSV is used, or if partial results are made available to
> the voters before most of them cast their approval ballots.
>
> Suppose that we have a three candidate cycle. How effective is Approval
> compared to Condorcet in this setting?
>
> In this setting, Approval voters may have a hard time applying Strategy A,
> especially if all of the candidates appear to have nearly equal support at
> all ranks.
>
> In this case Approval voters should ask themselves if their middle
> candidate is better or worse than half way between the other two
> candidates. If better, then approve, otherwise, not.
>
> In the borderline case, go with the decision of a friend, or wait for
> partial results to come out (if possible).
>
> If none of these possibilities are available, flip a coin. If the coin
> flip result gives you a bad feeling, go the other way. Your subconscious
> is wiser than you think.
>
> But let's consider the worst possible case: you have absolutely nothing to
> help you decide. Then just approve your favorite only. As we showed in a
> recent posting this is exactly as likely (in this zero info three
> candidate case) to work in your favor as approving both favorite and
> middle.
>
> In fact, we showed that as long as you approved your favorite and did not
> approve the candidate you considered worst, then given that your ballot is
> pivotal, there is a two thirds probability that your approval ballot will
> tip the election outcomein a direction that you consider favorable.
> [Satisfaction of the Participation criterion guarantees that it cannot
> make the outcome worse.]
>
> [If you make your decision on the basis of any information at all, this
> 2/3 probability is improved drastically.]
>
>
> So, by way of comparison, let's see if Condorcet can match this:
>
>
> Suppose that your sincere preference ballot is A>B>C, and that there is a
> cycle among these candidates. There are two possible directions for the
> cycle:
>
> Case I. A beats B beats C beats A.
> Case II. (the reverse of case I): A beats C beats B beats A.
>
>
> What is the setup that would put two of these candidates in a Condorcet
> near tie?
>
> The two weakest defeat strengths would have to be within one of each
> other.
>
> Case I.i The strong defeat is A>B.
>
> Subcase I.i.a The B>C defeat is equal to the C>A defeat.
> In this subcase Condorcet gives the win to A.
> Your ballot neither helps nor harms.
>
> Subcase I.i.b The B>C defeat is stronger than the C>A defeat by one.
> (Same result as previous case)
>
> Subcase I.i.c The B>C defeat is one weaker than the C>A defeat.
> In this subcase your ballot changes the winner from
> candidate C to A, definitely in your favor.
>
>
> Case I.ii The strong defeat is B>C.
>
> Subcase I.ii.a The A>B defeat is equal to the C>A defeat.
> In this subcase your ballot changes the winner from
> candidate B to A, in your favor.
>
> Subcase I.ii.b The A>B defeat is one less than the C>A defeat.
> After your ballot is taken into account B is still
> the winner: no help, no harm.
>
> Subcase I.ii.c The A>B defeat is one greater than the C>A defeat.
> A is the winner before and after your ballot is
> counted. No help, no harm.
>
> Case I.iii The strong defeat is C>A.
> In all three subcases of this case the two weak defeats are
> both increased by the same amount (one) so the winner C is
> not changed (no help, no harm).
>
> Case II.i The cycle is A>C>B>A and A>C is the strong defeat.
>
> Your ballot does not affect the result in any of the three subcases
> of Case II.i, because it does not change either of the two weak
> defeats ( C>B and B>A ) since they are both contrary to your ballot
> (still A>B>C).
>
> Case II.ii Cycle A>C>B>A and C>B is the strong defeat.
>
> Subcase II.ii.a The A>C and B>A defeats are equal in strength.
> Your ballot changes the winner from C to A.
>
> Subcase II.ii.b The A>C defeat is one less than the B>A defeat.
> The winner remains C.
>
> Subcase II.ii.c The A>C defeat is one greater than the B>A defeat.
> The winner remains A.
>
> Case II.iii Cycle A>C>B>A and B>A is the strong defeat.
>
> Of the three subcases, the only one that your ballot improves is
> the one in which A>C is one weaker than C>B. Your ballot improves
> the winner from C to B.
>
>
> Of the eighteen cases, your ballot only improves the result in four cases.
> Of course, your favorite was already the winner in six of those cases, so
> no improvement was possible. So taking that into account, we can say that
> your ballot improved the result in four of the twelve possible cases,
> about half as effective as Approval.
>
> Of course we didn't consider the use of truncation in Condorcet. But
> that's only fair, since the advantage of Condorcet over Approval is
> supposed to be that you can vote your sincere preferences without loss of
> voting power.
>
> This little case by case study seems to show that this supposition is not
> true, at least in three candidate cycle case that we are considering here;
> use of fully ranked ballots is less powerful than ballots that rank two of
> the three candidates equally (i.e. approval ballots).
>
> Forest
>
>
> ------------------------------
>
> Message: 3
> Date: Tue, 1 Feb 2005 17:28:02 -0800 (PST)
> From: Forest Simmons <simmonfo at up.edu>
> Subject: [EM] apology for "no subject" posting
> To: election-methods-electorama.com at electorama.com
> Message-ID: <Pine.LNX.4.61.0502011725020.11856 at lhotse.up.edu>
> Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed
>
> That no subject posting was just a slip of the Return key while scrolling
> down the EM digest. Sorry for the bother.
>
> Forest
>
>
>
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