[EM] Variable Inferred Approval Sorted Margins Elimination
C.Benham
cbenham at adam.com.au
Thu Jun 20 09:15:32 PDT 2019
Ted,
I don't see the two methods (VIASME and Smith/IBIFA ) as being in
competition with each other because they use
two very different types of ballot and and VIASME is probably much
harder to explain and sell.
> Smith/<something IBI> at least has the benefit of satisfying
> later-no-help ...
I'm afraid not. IBIFA fails Later-No-Help because adding a lower (or
"later") preference (i.e. rating another candidate X
above Bottom) can trigger another (say a second) round that is won by a
candidate (not X) you prefer to the one (also not X)
who would have otherwise won (say in the first round).
I thought of a possible kludge to try and fix that but it makes the
method much more complicated and and less Condorcet
efficient.
*(Say we are using 3-slot IBIFA.) We consider the IBIFA winner A to be
provisional. Then we truncate all the ballots below A
and if A is still the IBIFA winner we elect A.
But if instead there is a new IBIFA winner B, we un-truncate the ballots
below A and truncate below B and if B is still the
IBIFA winner then we elect B.
But if instead there is a new IBIFA winner C then repeat the process. If
we run out of candidates or a previous provisional
winner appears, then we simply elect the most approved candidate.*
A very ugly answer to a question no-one was asking, and I'm not even
completely sure it works. Median Ratings methods
(such as Bucklin and MJ) do meet Later-no-Help. Arguably it is
desirable that Later-no-Help and Later-no-Harm should
either both be met (like IRV) or both failed (like IBIFA and Condorcet
methods). Otherwise you either get a random-fill
incentive (yuck) or a very strong truncation (or only use the top and
bottom rating slots) incentive.
And complying with Later-no-Help is one of the properties that Woodall
has proved is incompatible with Condorcet, so
"Smith/ anything" can't meet it. The other criterion compliances in the
same boat are Later-no-Harm, Particpation,
Mono-raise-random, Mono-raise-delete, Mono-sub-plump, Mono-sub-top.
http://groups.yahoo.com/group/election-methods-list/files/wood1996.pdf
> Election 6:
> bca 3
> bac 2
> cab 3
> cba 2
> abc 3
> acb 2
>
> Theorem 2 says that if an election rule satisfies Condorcet's
> principle, then it cannot possess any of the seven properties that are
> crossed in the column headed 2 in Table 1.
> This is a lot to prove. Fortunately most of it can be proved by
> considering variants of Election 6 above. The only bit that cannot is
> the incompatibility of Condorcet with
> participation; this is proved by Moulin2, and I shall not attempt to
> reproduce his proof here. The following proof of the rest of Theorem 2
> invokes the axioms of symmetry
> and discrimination, for a precise statement of which see Woodall4.
>
> So suppose we have an election rule that satisfies Condorcet. By
> symmetry, the result of this rule applied to Election 6 above must be
> a 3-way tie. But by the axiom of
> discrimination, there must be a profile P very close to the one in
> Election 6 (in terms of the proportions of ballots of each type) that
> does not yield a tie. So our election rule,
> applied to profile P, elects one candidate unambiguously; and there is
> no loss of generality in supposing that this candidate is a. However,
> there are ways of modifying the
> profile P so that c becomes the Condorcet winner, so that our election
> rule must then elect c instead of a. This happens, for example, if all
> the bac ballots are replaced by a;
> and the fact that this causes c to be elected instead of a means that
> our election rule does not satisfy mono-raise-random,
> mono-raise-delete, mono-sub-top or mono-sub-plump.
> It also happens if all the abc ballots are replaced by a, and this
> shows that our election rule does not satisfy later-no-help.
>
> To prove that our election rule does not satisfy later-no-harm, it is
> necessary to consider a slight modification of the profile in Election
> 6, in which the second and third choices
> are deleted from all the abc, bca and cab ballots. Again, our election
> rule, applied to this profile, must result in a 3-way tie. But again,
> there must be a profile P' very close to this
> (in terms of the proportions of ballots of each type) that does not
> give rise to a tie, and we may suppose that our election rule elects a
> when applied to profile P'. But if we replace
> the a ballots in P' by abc, then b becomes the Condorcet winner, and
> so must be elected by Condorcet's principle; and this shows that our
> election rule does not satisfy later-no-harm.
> Together with the result of Moulin2 already mentioned, this completes
> the proof of Theorem 2, that an election rule that satisfies Condorcet
> cannot satisfy any of the seven properties
> crossed in the column headed 2 in Table 1.
>
Chris Benham
On 20/06/2019 5:20 am, Ted Stern wrote:
> Just as I'm warming up to Smith/Relevant-Ratings (or Smith/IBIFA), you
> introduce another method. :-)
>
> This seems to be in the same vein as MinLV(erw)SME.
>
> I like the general idea, but would prefer to avoid doing multiple
> tabulations as that makes the method not precinct summable.
>
> Smith/<something IBI> at least has the benefit of satisfying
> later-no-help and mono-raise without requiring multiple passes through
> the ballots.
>
> On Wed, Jun 19, 2019 at 10:59 AM C.Benham <cbenham at adam.com.au
> <mailto:cbenham at adam.com.au>> wrote:
>
> This is my favourite Condorcet method that uses high-intensity
> Score ballots (say 0-100):
>
> *Voters fill out high-intensity Score ballots (say 0-100) with
> many more available distinct scores
> (or rating slots) than there are candidates. Default score is zero.
>
> 1. Inferring ranking from scores, if there is a pairwise beats-all
> candidate that candidate wins.
>
> 2. Otherwise infer approval from score by interpreting each ballot
> as showing approval for the
> candidates it scores above the average (mean) of the scores it gives.
> Then use Approval Sorted Margins to order the candidates and
> eliminate the lowest-ordered
> candidate.
>
> 3. Among remaining candidates, ignoring eliminated candidates,
> repeat steps 1 and 2 until
> there is a winner.*
>
> To save time we can start by eliminating all the non-members of
> the Smith set and stop when
> we have ordered the last 3 candidates and then elect the
> highest-ordered one.
>
> https://electowiki.org/wiki/Approval_Sorted_Margins
>
> In simple 3-candidate case this is the same as Approval Sorted
> Margins where the voters signal
> their approval cut-offs just by having a large gap in the scores
> they give.
>
> That method fulfils Forest's recent 3-candidate, 3-groups of
> voters scenarios requirements, resists Burial
> relatively well and meets mono-raise. The motivation behind this
> version is to minimise any disadvantage
> held by naive (and/or uninformed) sincere voters.
>
> Chris Benham
>
> *Forest Simmons* fsimmons at pcc.edu
> <mailto:election-methods%40lists.electorama.com?Subject=Re%3A%20%5BEM%5D%20What%20are%20some%20simple%20methods%20that%20accomplish%20the%20following%0A%20conditions%3F&In-Reply-To=%3CCAP29onet%2BO9hCZJ6hvNnnpUWNyrDkKa9xFXrX5P-RPoF6ndtfw%40mail.gmail.com%3E>
> /Thu May 30 /
>
>> In the example profiles below 100 = P+Q+R, and 50>P>Q>R>0.
>>
>> I am interested in simple methods that always ...
>>
>> (1) elect candidate A given the following profile:
>> P: A
>> Q: B>>C
>> R: C,
>>
>> and
>> (2) elect candidate C given
>> P: A
>> Q: B>C>>
>> R: C,
>>
>> and
>> (3) elect candidate B given
>> P: A
>> Q: B>>C (or B>C)
>> R: C>>B. (or C>B)
>>
>
>
>
>
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