[EM] Yee/B.Olson Diagram Remarks

[Juho Laatu]

In the Yee/B.Olson diagrams Condorcet
methods give quite ideal results. I
proposed ages ago that one might
study also voter distributions that
give cyclic preferences. That would
show also some differences between
different Condocet methods. I'll try
to draft some simulation scenarios.

In a typical simulation there is one
"heap" of voters that can move around.
Another approach would be to have a
smaller heap of voters at the position
of each candidate. This can be said to
be natural. Every candidate is seen to
represent some supporter group or
party, and there is a concentration of
voters close to each candidate.

In order to move the balance of voters
in the diagram area one can add one
larger and flatter heap of voters to
this. Then one can move this larger
heap so that the average voter (or
median voter) moves around in the
diagram (average location should be
easier to count but median could be
more interesting as a diagram). This
way one can draw all the pixels of
the diagram.

Now to cyclic preferences. We can
rotate all the small heaps around the
centre of the diagram (few degrees) so
that each small heap is no more exactly
where the candidates are but next to
them. This way one can get also
circular preferences. This is still
"natural" in the sense that the
candidates may well not represent the
median opinion of their "own party" but
they (or their supporters) may be
biased in one direction. (The larger
heap can again be moved around to move
the average/median voter spot.)

One can generalize this style so that
in addition to having a set of
candidates that can be drawn anywhere
on the diagram one could have also
limited number of small heaps of voters
that can be put anywhere on the diagram
(and shown in the diagram using some
special marks).

This is just one approach to richer
modelling of the voter space. The small
heaps could typically be of same size
to keep the diagram easy to grasp. The
larger heap is used just to move the
overall balance of the voters. There
could be also other ways to move the
balance but this one is at least quite
simple and understandable.

The target is to be able to model also
some slightly more complex voter
distributions than the basic normal
distribution of voters in a two
dimensional space. And to be able to
make more detailed comparisons, e.g.
between different Condorcet methods.

Juho