[EM] election strategy paper, alternative Smith, web site relaunch

[C.Benham]

James Green-Armytage wrote (20 Nov 2010):
<snip>

> In addition to the nine methods listed above, I tried some of my 
> analyses with six other Condorcet methods: beatpath, ranked pairs, 
> Smith/Hare, alternative Smith, and two versions of cardinal pairwise. 
> Beatpath and ranked pairs generally seem to perform like minimax, and 
> cardinal pairwise usually but not always performs somewhat better than 
> these, but the really striking news in my opinion is how well the 
> Hare-Condorcet hybrids perform.
>
> That is, given a preliminary analysis, they seem to be as resistant to 
> strategic voting as Hare (and possibly slightly more resistant), and 
> they are distinctly less vulnerable to strategic nomination (because 
> they are Smith efficient, and therefore only vulnerable to strategic 
> nomination when there is a majority rule cycle). So, for single-winner 
> public elections, alternative Smith and Smith/Hare seem to have a lot 
> to recommend them, i.e. the combination of Smith efficiency with 
> strong resistance to both types of election strategy.
>
> I should define these methods here, for clarity. Smith/Hare eliminates 
> all candidates not in the Smith set (minimal dominant set, i.e. the 
> smallest set of candidates such that all members in the set pairwise 
> beat all members outside the set), and then holds an IRV tally among 
> remaining candidates. This method has been floating around this list 
> for a while, yes? Does anyone know of an academic publication that 
> mentions it? I seem to remember reading something that said that it 
> had been named after a person at some point, but I no longer know 
> where I read that.
>
> Alternative Smith is a closely related method, which Nic Tideman made 
> up when he was writing Collective Decisions and Voting. It (1) 
> eliminates all candidates not in the Smith set, then (2) eliminates 
> the candidate with the fewest top-choice votes. Steps 1 and 2 
> alternate until only one candidate remains. (See page 232 of the 
> book.) I focus on this rule rather than Smith/Hare in the paper, 
> because I find it marginally more elegant, but the difference between 
> the two is very minor.
>

James,
We discussed these  "Hare-Condorcet hybrids" on EM in the months of 
October and
November 2005. Then I quoted Douglas Woodall's demonstration that both 
the versions
you discuss fail Mono-add-Plump and  Mono-append.


> abcd 10
> bcda  6
> c     2
> dcab  5
>
> All the candidates are in the top tier, and the AV winner is a.  But
> if you add two extra ballots that plump for a, or append a to the two
> ballots, then the CNTT becomes {a,b,c}, and if you delete d from all
> the ballots before applying AV then c wins.


Translating to a more familiar EM format:

10: A>B>C>D
06: B>C>D>A
02: C
05: D>C>A>B

All candidates are in the Smith set  (Woodall's "Condorcet-Net Top 
Tier"), and the Hare
(aka "Alternative Vote", aka IRV) winner is A. 

But if you add 2 ballots that bullet-vote (plump) for A, or change the 
two C ballots to C>A,
the Smith set becomes {A B C}, and if you delete D from all the ballots 
from all the ballots before
applying Hare (i.e. properly "eliminate" D and not just disqualify D 
from winning) then C wins.

Smith,Hare (which Woodall called "CNTT,AV") meets those criteria and has 
a simpler algorithm:

> Begiinining with their most preferred candidate, voters strictly rank 
> however many candidates they wish.
> Before each (and any) elimination, check for a candidate X that 
> pairwise beats all  (so far uneliminated)
> candidates. Until such an X appears, one-at-a-time eliminate the 
> candidate that is voted favourite
> (among uneliminated candidates) on the fewest ballots. As soon as an X 
> appears, elect X.
>

So why put up with failures of  mono-add-plump and mono-append? What 
advantage (if any) do you think
the two versions you discuss have over Smith,Hare to compensate for that?

Chris Benham