[EM] The general form of Quick Runoff

[C.Benham]

Kevin,

Quoting myself:

>Why not order the candidates by DSC (the reverse of the DSC disqualification order)?
>
>Wouldn't that version simply dominate (in terms of desirable criterion compliances) the QR 
>you've defined (that uses the FPP order)?
>
>Compared to plain DSC it seems to just gain compliance with Condorcet(Gross) Loser in
>exchange for losing compliance with Irrelevant Ballots.
>  
>

Thinking about it a bit more, plain DSC would have other criterion 
compliance advantages over the DSC-based version of
QR besides just Irrelevant Ballots. 

I have in mind Participation, probably even still Mono-add-Plump, and  
Mono-Raise.

>But in contrast to e.g. SPST, a small center candidate can't be so easily
>sunk by the presence of a stronger but futile extremist candidate. So
>I do see improvement here.
>

I'd be interested in seeing a 3-candidate example where it gives a 
different result from SPST.


Chris Benham



Kevin Venzke wrote (24 May 2010):

Hi Chris,

--- En date de : Lun 24.5.10, Chris Benham <cbenhamau at yahoo.com.au <http://lists.electorama.com/listinfo.cgi/election-methods-electorama.com>> a écrit :
>/ Kevin,
/>/ 
/>/ This new "Quick Runoff" (QR) method suggestion of yours
/>/ does nothing to shake my opinion
/>/ that IRV is the best LNHarm method.
/
Sorry you feel that way. If you expect center squeeze I can't see a
reason to use IRV. It can almost guarantee to get it wrong in some 
scenarios. I would mainly want to use IRV if I thought there wouldn't
be anything like a "center" option, in which case it's a sound idea to
eliminate the first preference loser.

>/ Without bothering to make an example, it seems obvious that
/>/ it fails Mono-add-Plump.
/
Yes, I think it does.

To my mind the important thing is that the criterion failures can't be
easily exploited. In general, if you want to win, you want as many
first preferences and as many majority wins as possible.

>/ "(It's conceivable that another way of ordering the
/>/ candidates could
/>/ preserve all the properties plus clone independence, but
/>/ I'm not very
/>/ optimistic at the moment.)"
/>/ 
/>/ Why not order the candidates by DSC (the reverse of the DSC
/>/ disqualification order)?
/>/ 
/>/ Wouldn't that version simply dominate (in terms of
/>/ desirable criterion compliances) the QR 
/>/ you've defined (that uses the FPP order)?
/
It is possible but I would have to check it. It would certainly be
harder to explain that way, even if so.

>/ Compared to plain DSC it seems to just gain compliance with
/>/ Condorcet(Gross) Loser in
/>/ exchange for losing compliance with Irrelevant Ballots.
/
Unfortunately QR doesn't do well by a lot of criteria, and I'm lacking
a criterion that explains why I find it so promising.

It doesn't gracefully handle large numbers of candidates, even if it can
be generalized for them, but I guess this shouldn't be a big surprise
coming from me, as I don't find large numbers of nominees to be a 
promising situation in any case.

But in contrast to e.g. SPST, a small center candidate can't be so easily
sunk by the presence of a stronger but futile extremist candidate. So
I do see improvement here.

I will put together some comparative examples, I think, in particular
due to your doubt when comparing it to DSC. I also have some numbers that
suggest that the majority rule (vs. ending with a simple elim/transfer),
while it is less Condorcet-efficient, not only retains Plurality in
exchange, but is also less likely to fail MD.

Thanks for your comments.

Kevin



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