[EM] Head to Head Comparison of Election Methods

[Paul Dumais]

Blake Cretney wrote:

> > >
> > > What is defeating the folk song is those cumulative margins from all
> > > the country songs in the running.  If there were 1000 country songs in
> > > the running, then, based on cumulative margins, it would look like the
> > > folk song was a terrible choice.  But this would just be the result of
> > > voters' genre preference combined with the number of each being
> > > nominated, not an actual change of attitude on anyone's part towards
> > > Folk in general or the song in particular.
> >
> > You make some very good points. It seems to me that Dumais will have
> > "problems" when similar choices are introduces because it treats all
> > candidates as being dissimilar to a certain degree. Path voting on the
> > other hand has "problems" when candidates are viewed as dissimilar yet
> > the voting information treats them as being similar. I will need some
> > help to develop good examples for the above "problem" with path voting
> > (if they exist) because they would involve situation involving 4 or more
> > candidates (with the "problems" potentially getting worse).
> 
> What would you consider a problem situation?  Is it one where the
> Borda count of the PV winner is very low compared to some of the
> losers?

I suppose. I consider it a "problem" when the path winner is eliminated
under Dumais such as in the first round with a borda count that is very
low compared to several other candidates who are not eliminated.

> > Perhaps
> > Steve Eppley's program would help us to do some statistical analysis on
> > the space of possible outcomes.
> 
> I have seen the program.  I think the task you describe is
> significantly different from what the program is now doing.
> 
> > Does Steve provide this program for
> > others to try? Particularly, I'm interested in determining how serious a
> > problem Dumais voting encounters with similar candidates. I would also
> > like to examine the space of possibilities where intuitively I see some
> > severe problems (my intuition could be very wrong).
> 
> Consider the following example:
> 
> 51 A B C
> 49 B C A
> 
> This is often used as a Borda bad example.  If you see B and C as
> clones, it clearly comes to the wrong conclusion.  But if you don't,
> if the candidates really are independent, as Borda assumes, the result
> makes perfect sense.  That is, if they are independent, it makes sense
> to say that A doesn't do as well as B does against C, and this
> information should be used against A.
> 
> Since there is no way to tell which of a voter's opinions are
> independent, even for rated ballots, there will never be a perfect
> solution to this problem.
> 
> Path Voting seems to be based on getting as much information as
> possible out of the ranked ballot, without assuming any level of
> independence in voter choices.  This means that sometimes, where there
> is more independence, a method that assumes this will come to a better
> conclusion.  However, a method that assumes more independence will
> also have these problems:
> 
> 1.  The method will be more likely wrong when the Path Voting
> assumption is closer to correct.
> 2.  If the method differs little from the assumptions of Path Voting,
> it will have only a slight advantage over it, even if its assumptions
> are closer to correct.
> 3.  Methods that assume levels of independence end up with clone
> problems.  These are fairly bad strategy problems.  As well, the
> strategies they encourage often make the method's assumptions further
> from true.  For example, Borda assumes independence.  The result is a
> method that encourages clones.  This reduces independence.
> 4.  If levels of independence are found for one group at one time,
> they may not hold for a different group or a different time.
> 5.  The "correct" level of independence search will result in methods
> that are designed arbitrarily.  Just as happens if people use
> positional methods, and allow themselves to assign arbitrary points
> for various ranks.
> 
> >       Here's my intuitive arguments (feel free to ignore this wishy-washy
> > talk). It seems impossible to tell before hand the impact of introducing
> > multiple similar candidates. With the examples we've seen, it seems that
> > intoducing clones would rarely help the clone (if ever). So as long as
> > candidates representing a certain ideal (like country music) do not have
> > a predictable advantage by introducing many candidates and candidate
> > introduction has a cost to it, then intoducing clones of yourself would
> > be rare.
> 
> I agree that introducing clones of yourself would be rare.  Instead
> voters and candidates would work to avoid splitting the vote.
> 
> >       Path voting treats much of the voting information as not important.
> > This may be good where there are many clones, but where candidates are
> > quite different from each other, we could get situations where the
> > cumulative effect of many votes with margins less than the smallest path
> > margin for a givin path winner are ignored. This could produce grossly
> > unfair results. So the head to head winner of Dumais vs Path may very
> > well come down to which method has the most severe "problems" and how
> > often do these problems occur in real situations (but we should look at
> > factors such a simplicity, meaningfullness, etc). Some software will
> > probably help us discover this more quickly (via statistics) than we
> > could by providing isolated examples.
> >
> > > Let's imagine that the nominating committee dislikes folk music, they
> > > can ensure folk is eliminated just by nominating more country songs,
> > > while still appearing to give this genre a fair chance.
> >
> > Polling information would have to be quite accurate. Introducing clones
> > could very well help folk music under different circumstances. In any
> > case, a nominating committee perhaps shouldn't be used for Dumais.
> 
> It wouldn't have to be all that accurate, in the sense that small
> differences between expected and actual outcome won't tend to cause
> the strategy to back-fire.  I am woried about strategies like this,
> because they would be easier to orchestrate than convincing large
> numbers of people to vote insincerely.
> 
> I see the nominating committee as an important example because
> referendums might often be presented on this basis.
> 
> > > To take this back to the world of politics, if a legislative body is
> > > holding a vote between several proposals using Dumais, then it is
> > > possible for people to cleverly nominate similar proposals with the
> > > hope of having the above effect.
> >
> > They would have to be very clever.
> 
> Particularly for members of legislative bodies ;)
> 
> > > If you are unaware of voter preferences, and just want to torpedo a
> > > particular proposal, there is a more direct way.  Just nominate other
> > > similar proposals.  I'll show this vote splitting effect for the music
> > > example.
> > >        2  1  0 -1 -2
> > > I   35 C  F1 F2 F3 R
> > > II  40 F1 F2 F3 R  C
> > > III 25 R  C  F1 F2 F3
> > >
> > > C 70-80+25>0
> > > R -70-40+50<0
> > > F1 35+80>0
> > > F2 40-25>0
> > > F3 -35-50<0
> > >
> > > More folk songs have made the rock song seem like a worse choice.
> > > The effect is that the rock song is eliminated.  This weakens the
> > > standing of folk, since it won against rock; in general, it is bad to
> > > have alternatives that you defeat eliminated.  This effect is also
> > > what causes the violation of monotonicity.
> > >
> > > I   35 C  F1 F2
> > > II  40 F1 F2 C
> > > III 25 C  F1 F2
> > >
> > > It is obvious that the country song now wins, since it is the first
> > > choice of a majority among the non-eliminated alternatives.
> > >
> 
> > I don't understand your above argument. How can you help a chosen
> > candidate by introducing clones of a candidate without having good
> > polling information before hand? It seems good polling information is
> > required for the above example as well.
> 
> You can't help a chosen candidate by introducing clones of it (at
> least it doesn't happen often).  The example shows how you can defeat
> a candidate you particularly dislike, however.  In the above example,
> the mischievous nominator was trying to avoid a Folk win, not
> particularly to cause a Country win.
> 
> > I would like to introduce other arguments against the use of path
> > voting. Isn't it difficult to impliment? Given 100 candidates, how long
> > would it take you to find a winner (without a computer).
> 
> You can start by reducing to the Smith set.  Non-Smith set candidates
> have no effect on the result.
> 
> I have in the past suggested a couple of convenient ways to find a
> winner by hand.  One I called the Goldfish algorithm, and is good if
> you have a matrix.  The other way (which is easy if you draw a
> diagram) is to follow this procedure:
> 
> 1.  Reduce to the Smith set.  If all a candidate's paths to the Smith
> set have dropped members, then it is considered no longer in the Smith
> set.
> 2.  Drop the victory with the smallest majority.  Once a victory has
> been dropped, it is no longer considered.
> 3.  Return to step 1.
> 
> This is the method I use to find a winner quickly by hand.
> 
> > How easy is it
> > to state the method in such a way that people will understand and trust
> > this method? How meaningful is a path anyway? To say that there is a
> > path from A>B>C>D uses the information B>C and C>D. Is it valid to use
> > this information to support the choice of A as the winner? Isn't this
> > information arbitrary as B>C and C>D information was never meant to be
> > used to support or not support A. How would voters feel knowing that
> > such information was used to choose A as the winner while information
> > such as B>A and C>A was ignored (except that it was less than the
> > margins in B>C and C>D)?
> 
> Well, if you agree that A>B provides evidence that A is better than
> B, then it follows that
> A>B B>C C>D D>E
> provides evidence that A is better than E, since if the majority is
> correct in each of these cases, this is inevitably true.  As well, the
> stronger these majorities are, the better evidence it seems to be.
> Path Voting provides a simple way to decide a winner based on this
> information.
> 
> That's my non-rigorous, intuitive argument.
> 
> > Dumais provides intuitively valid information
> > in quantities that are easily understood (ie A is preferred 347/500 when
> > compared to all candidates).
> 
> Our intuitions differ on this point.  Note that the number you say is
> intuitive, 347/500, does not actually directly decide the election.
> It is only when this is combined with eliminations that we get Dumais.
> 
> ---
> Blake Cretney
> See the EM Resource:  http://www.fortunecity.com/meltingpot/harrow/124
> My Path voting Site:  http://www.fortunecity.com/meltingpot/harrow/124/path



-- 
Paul Dumais