[Election-Methods] strategic voting and strategic nomination

[James Green-Armytage]

Chris Benham <cbenhamau at yahoo.com.au> writes:
>In Ireland it is used to elect the President. The Irish lower house uses
>multi-winner
>STV.  UK mayoral elections mostly use the  "Supplementary Vote". From
>Wikipedia:

Ah, my mistake. Thank you for the corrections. I think that I just tried
to copy that information from the wikipedia page on IRV, but perhaps I did
a sloppy job (or is that page wrong?).
>
>Of course it is equivalent to IRV when there are three candidates, but is
>otherwise awful.

Okay; I can point out that these elections use supplementary vote, which
can be viewed as a variant on IRV.
>
>Regarding MinMax in your paper you wrote:
>"The winner is the candidate whose worst pairwise loss (if any) is least
>bad;..."
>You don't define here how you measure "least bad". Later you give this:
>"Minimax
>To calculate the winner
>1. Form a pairwise matrix. Form the N by 1 vector MAXBEAT, where MAXBEATx
>is the
>greatest number of votes against x in any pairwise contest, i.e.
>MAXBEATx=max(PM:,x). The
>candidate with the smallest value in the MAXBEAT vector is the winner."
> 
>This make no reference to "pairwise losses", so isn't it 
>"MinMax(Pairwise Opposition)" that
>*fails* the Condorcet criterion?
>[ http://nodesiege.tripod.com/elections/#methmmpo
>]http://nodesiege.tripod.com/elections/#methmmpo

These seem like subtle distinctions, as my program doesn't generate any
incomplete ballots or preferences. I'm a little rusty on this, but I do
think I see how this algorithm could fail Condorcet given incomplete
ballots. I seem to remember thinking, while I wrote the minimax strategy
program, that allowing incomplete ballots wouldn't make strategy any
harder or easier, but that was about a year ago, and I don't really
remember my full logic. But yes, modifying the programs so that they can
handle incomplete preferences would be a logical step.

Another thing I really would like to do is write programs for beatpath and
ranked pairs, but I haven't got around to that yet. The minimax strategy
program was the hardest one for me to write, and the one in which the
possibility of an error is most real (if you see how I describe the
program in the paper, it is rather convoluted). I think that I can
eventually write programs for beatpath and ranked pairs, but I expect it
to be tricky, so I've put it off while I work on other (unrelated)
projects. Cardinal pairwise also seems to be extremely hard to analyze in
this way; I can write a program that approximates its vulnerability, but
getting it dead on is very challenging. Multiple-winner STV is another
hard one; I think I know how the program should work in principle, but
writing it may be a bit of a headache.  

Kristofer Munsterhjelm <km-elmet at broadpark.no> writes:
>That's interesting, because optimal strategizing in IRV has been found 
>to be NP-complete ("The Computational Difficulty of Manipulating an 
>Election"). So, in a sense, your simulations reflect this (and that IRV 
>strategy is closer to the difficult part/phase transition of the 
>NP-complete domain; that is, it's not just the easy instances).
>
Thank you for the reference; this looks like an interesting paper. 

my best,
James


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