Abstract:
In this dissertation we will analyze the proximity spatial models for cumulative
voting. We will show that the cumulative voting method, with its
plumping strategy, provides a greater chance of minority representation in
the elected body than often occurs in multimember districts elected by plurality.
Using our cumulative voting heuristic, we identify conditions necessary
for a Nash equilibrium to exist when voters’ ideal points are normally
distributed with N (0, 1). We will show, through a proposition and proving
it, than under our cumulative voting heuristic, candidates tend to adopt
centrifugal positions, away from the median voter. With this in mind, we
will place two candidates away from the median, on the opposite sides, and
investigate conditions necessary for a Nash equilibrium to exist. We will accomplish
this by first placing a third candidate within an neighborhood of
either of the other two candidates and then let him assume positions anywhere
on R1
, the single predictive dimension space. From the first analysis
we will develop an equation whose solutions provide the only possiblity for a
Nash equilibrium to exist. Using Numerical Analysis techniques we will approximate
those solutions by a nice elementary function whose properties we
know. From the second analysis, we will derive mathematical models which
we analyze to establish intervals of β for which a Nash equilbrium exists.
We will then extend our analysis to a more plausible distribution for the
cumulative voting method, the ”double Normal” distribution. The problem
model we developed in this case will be very complex and hence necessitate
analysis via simulation. Through this simulation model we will illustrate
the electoral potential of cumulative voting to yield fair representation when
plurality voting does not.
