[EM] Variable Inferred Approval Sorted Margins Elimination

C.Benham cbenham at adam.com.au
Thu Jun 20 09:15:32 PDT 2019


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

*(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.


> 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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