[EM] Tallying visualization for Condorcet methods?

[Jan Kok]

On 2/5/06, Scott Ritchie <scott at open-vote.org> wrote:
> On Sun, 2006-02-05 at 20:55 -0600, Paul Kislanko wrote:
> > Jiri Räsänen asked:
> > >
> > > Hello everyone,
> > >
> > > I am new to this list. I am interested for possible ways to visualize
> > > the votes tallying and the results for Beatpath method.

An interesting question, that I haven't found a satisfactory answer to.

> > > Previously I have done some campaigning for the use of STV and found
> > > out that once I could draw the graphical version of the vote
> > > counting,
> > > people would get the feeling that they understand what's going on.
> > > Before this, when explaining the system, people were scratching their
> > > heads.

What graphics do you use for visualizing STV?

For IRV, I use a pie chart showing what percent of the 1st-choice
votes each candidate got.  Then, I subdivide the 1st-choice segments
to show the fraction of 2nd-choice votes.  For example,

39 A>B
10 B>A
10 B>C
41 C>B

The pie chart would have the following sections ("|" marks major
section boundaries):

| A>B | B>A, B>C | C>B

This diagram makes it easy to see who wins (the C section + B>C
subsection make up >50% of the pie).

It's also easy to see how at least 11 of the C>B faction should vote
B>C instead, in order to make the compromise candidate, B, win.

> > > For Beatpath this might be a harder thing to do, but I'm sure there
> > > must be some ways to present the vote counting in a visual
> > > and dynamic
> > > way that is sensible for the functioning of the system.

The pie chart can also be used for visualizing Condorcet elections,
but I find it only slightly useful for three candidates, and useless
for more than three candidates.  If I want to explain how Condorcet
elections are counted, I just show how to fill out a preference
matrix.  I explain that it is like a round-robin tournament.  If 10
people rank A over B and 5 people rank B over A, then A beats B 10 to
5.  Draw a circle around the winning score (e.g. the 10) of each
pairwise contest.  If one candidate beats all the other candidates
(there is a row in the preference matrix where all the numbers are
circled), that candidate wins.  Otherwise, as can happen in real-life
round robin sports tournaments, there is a circular tie.  Drop the
least defeat, etc.

> > > My personal experience is that people would go to the extreme
> > > to avoid
> > > thinking. As most of you propably have experienced people
> > > just bluntly
> > > saying "oh, that is too complicated" when you try to explain a voting
> > > system.  A good visualization can give a person a sense that he/she
> > > somehow grasps what's going on, although more comprehensive
> > > understangin may remain unaccomlished.
> > >
> > > For the matter of political reform in any instance outside computer
> > > scientist and mathematicians, I think a good visualization will be
> > > essential.
> > >
> > > I did a search on this list on visualization, but found not much
> > > useful. Has anyone of you privately been thinking of ways to
> > > visualize
> > > Beatpath or other Condorcet methods?
> >
> > I doubt that there's any way to graphically show the difference beteen
> > ranked-pairs and beatpath (for instance), but to just demonstrate how ranked
> > ballots show the preponderance of voters' opinions graphically, I used this
> > http://vmedia.rivals.com/uploads/1048/317514.gif
> >
> > In that "election" (really a "sports poll" about which is the best team)
> > there was a #1 and "everybody else", but the "everybody else" part is a
> > pretty good picture of why you need to analyze the ballots in various ways
> > (i.e. beatpath vs ranked pairs, minmax, etc.)
> >
> I'm sorry, I don't get it - what exactly does this graph mean?  The axis
> are unlabeled.

The axis labelled "#1", "#8", etc. is the ranks, i.e. 1st choice, 2nd choice.

The unlabelled axis that has different colors for each position
represents the various candidates.

The vertical axis (the height of the bars) shows the number of ballots
that had candidate X as Nth choice.

Cheers,
- Jan

P.S. This type of bar chart would be useful for visualing Bucklin vote
tallying, if the chart is rotated 180 degrees around the vertical
axis, and the heights of the bars are cumulative, i.e. the first row
heights are proportional to the number of ballots with candidate X as
first choice, the second row heights are proportional to the number of
ballots that have candidate X as first OR second choice, etc.