[EM] Amalgamation details, hijacking, and free-riding
fsimmons at pcc.edu
fsimmons at pcc.edu
Wed Aug 3 12:49:57 PDT 2011
So if the true preferences are
20 A>B
45 C>?
35 (something else),
the C supporters could spare 21 voters to vote A>C so that the amalgamated factions would become
41 A>C
24 C>?
35 (something else) .
I can see where it is possible for such a move to payoff, but it seems fairly innocuos compared to other
strategy problems like burial, compromising, chicken, etc.
In any case, it can only be a problem in methods that forget the ratings after the amalgamation and use
only the rankings (like DSC), because when two candidates are rated closely a small "hijacking" effort
could tip the balance and reverse the ranking of the two candidates in question.
On the "free rider" problem of some PR methods, what do you think about the following?
Because of its "free riding problem" Plurality is a fairly decent PR method in a perfect information
setting, as long as voters agree to randomize in order to take advantage of the free riding effect. For
example in a three winner election where the voter preferences are
60 A1>A2
25 B
15 C
If the A supporters agreed to toss coins and vote A! or A2 in the case of heads or tails, respectively,
then the winning slate would be {A1, A2, B}, the best possible outcome in this case.
So, in at least one PR method, the "free-riding" possibilities are essential for the fairness of the method.
In fact, that is the basic principle of Asset voting (for PR); the candidates share their assets so that
none will be wasted unnecessarily. Whether the voters or the candidates do the redistribution doesn't
natter in the perfect info case.
In the zero info case, free-riding doesn't work, so it can neither harm nor help.
So, I don't worry too much about it.
From: Jameson Quinn
> OK, that's what I thought. So, candidate hijacking does not work
> for any
> amalgamated "ballot blind" method, that is, a method which
> forgets which
> rating came from which ballot. However, on a non-ballot-blind system,
> including the ranking-based DSC which was the next step in your
> SODA-inspired "sequential play" method, it can work. Basically,
> it involves
> finding a faction a bit smaller than yours, and ranking its favorite
> candidate first. Since your faction is larger, you will be able
> to set the
> ranking of the remaining candidates, and you will gain the
> ballot weight of
> the smaller faction. Of course, you must be sure that the "false flag"
> candidate does not win. This is similar to Wodall free riding in PR.
>
> JQ
>
> 2011/8/1
>
> > To amalgamate factions so that there is at most one faction
> per candidate X
> > (in the context of range
> > style ballots) take a weighted average of all of the ballots
> that give X
> > top rating, where each ballot has
> > weight equal to one over the number of candidates rated equal
> top on that
> > ballot. The total weight of the
> > resulting "faction rating vector" for candidate X is the sum
> of the weights
> > that that were used for the
> > weighted average.
> >
> > Note that these faction rating vectors are efficiently
> summable. A running
> > sum (together with its weight)
> > is kept for each candidate. Any single ballot is incorporated
> by taking a
> > weighted average of the running
> > sum and the ballot, where the respective weights are those
> mentioned above.
> > For the running sum it is
> > the running sum weight. For the ballot it is zero if the
> candidate is not
> > rated top, and 1/k if it is rated top
> > with (k-1) other candidates..
> >
> > To combine two running sums for the same candidate take a
> weighted average
> > of the two using the
> > running sum weights, and then add these weights together to
> get the
> > combined running sum weight.
> >
> > If you multiply each faction rating vector by its weight and
> add up all
> > such products, you get the vector of
> > range totals.
> >
> > Of course Range as a method is summable more efficiently without
> > amalgamating factions, but other
> > non-summable methods, when willing to accept amalgamated
> factions, thereby
> > become summable.
> >
> > So, for example, we can make a summable form of Dodgson:
> >
> > (1) Use ratings instead of rankings.
> >
> > (2) amalgamate the factions.
> >
> > (3) let each candidate (with help from advisors) propose a
> modification of
> > the ballots that will created a
> > Condorcet Winner.
> >
> > (4) the CW that is created with the least total modification
> is the winner.
> >
> > Modifications are measured by how much they change the ratings
> on how many
> > ballots.
> >
> > For example if you change X's rating by .27 on 10 of the 537
> ballots of one
> > faction, and by .32 on 15
> > ballots from another faction, then the total modification is
> 2.7 + 4.8 =
> > 7.5
> >
> > The reason for the competition is that otherwise the method
> would be
> > NP-complete.
> >
>
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