[EM] Web interfaces and Condorcet scores

[Rob Speer]

On Sun, Oct 26, 2003 at 11:15:49AM -0800, Rob Brown wrote:
> Here is a UI I am working on for doing for ranking 
> candidates:    http://weblogz.com/voting/2000pres.html
> This demo is of course based on the 2000 presidential election, and allows 
> you to rank candidates with a (hopefully) friendly UI.  I avoided having 
> people manually assign numbers to candidates  (after all, they are sitting 
> in front of a perfectly good computer which can do that sort of thing 
> well!), and I tried using a little animation, which seems to help in making 
> it easy for voters to follow what they are doing.

This interface is *very nice*. I applaud you.

I've been working on a project similar to what you've been doing, as an
assistant to an MIT professor who wants to make preferential voting more
widely available. The idea of the project is to create a web site where
organizations (this is key; the Internet should _not_ be used for public
elections!) can hold reasonably secure elections using any election
method they choose. The "reasonably secure" part has, of course, turned
into the part of the project requiring the most research.

(The project has nothing to do with the MIT/Caltech Voting Initiative;
they're working on public elections, and kind of floundering at it from
what I can tell.)

One problem I've had in designing the web site from a usability aspect
is how to let people easily cast preferential votes. Text boxes to type
numbers into are inherently confusing, and reloading the page after
every vote would be frustrating and encourage people to truncate. I had
assumed that changing the display on the fly with JavaScript would also
be too confusing.

However, now that I've seen your interface, I find it amazingly
intuitive, and I'd like to ask your permission to use it in my project.

> Now I need to figure out how to display results, in a way that makes sense 
> to people.  The people I have talked to who are likely to use this system 
> want to see more information beyond just the final ranking of candidates -- 
> they want to see some kind of "score" or a graph.  They are used to web 
> based polls where you can see a nice little graph, showing how many voted 
> for which candidate.  Knowing whether an election was neck-and-neck or a 
> landslide is relevant information people should be able to see, I think.

I've thought about this too.

One display of information that I think could be useful is to have the
list of rankings, and show the vote margins between adjacent candidates
in the rankings. This is, of course, seriously glossing over the
details, but it does give a general idea of "how close" the election
was. "Bob is the winner; Bob defeated Sam by 17 votes; Sam defeated Jane
by 5 votes..."

The only worry would be if a Condorcet method could produce a ranking
where someone loses to the candidate directly below him, which would
confuse and alarm people by displaying a negative margin of defeat.
However, it seems that generally cycles are unrolled in such a way that
this does not happen.

Another possible display (and one that is more meaningful to the
outcome) is to show by how much each candidate lost to the winner.

> Another thing I tried was showing a score which is the sum of all margins 
> by which they beat (or lost to) every other candidate.  For instance, if 20 
> voters placed B above A, and 10 placed A above B, that would add 10 to B's 
> score and subtract 10 from A's score. Again, though, it may not correllate 
> with the Condorcet ranking, although for some reason my feeling is that 
> this type of score is "better" than a Borda count. (is there a name for 
> such a way of scoring?)

The Borda Count. :)

You can prove that the Borda count is equivalent to the "sum-of-margins"
ranking. The numbers will of course be different, but they will simply
be a shifted and scaled version of the Borda results.

The gist of it is this: you can think of a Borda ballot as giving each
candidate a point for each candidate they beat on that ballot. On a
five-candidate ballot that is fully ranked, for example, the top
candidate gets 4 points for beating 4 people, and the bottom candidate
gets 0 points for beating no one.

You could change the scoring method without changing the results by
giving a candidate a point for each candidate they beat, and -1 point
for each candidate they lose to. This would make the Borda scores on a
five-candidate ballot shift from 4, 3, 2, 1, 0 to 4, 2, 0, -2, -4. This
transformation is linear, so it cannot change the outcome when it is
added up.

When you add these scores over all the ballots, you get exactly the sum
of the victory margins.

-- 
Rob Speer