You could have refrained from personal attacks, just because you have more posts than I do does not give you free reign to insult others. I was a little stressed and impatient, but you were the one to launch in with the personal attacks (flames). If a slight deviation from the standard way of posting makes personal attacks from others acceptable, I will not be around here much longer. Since you are so curious, here is the first page of my dissertation.
Simultaneous Move Adaptive Parties in Multidimensional Spatial Elections
Dan X. Xxxxxxx
Department of Humanities and Social Science
California Institute of Technology
(danxxx@cco.caltech.edu)
Abstract
I examine a multidimensional spatial model in which two candidates compete. Instead of the standard game theoretic model though, I model candidates (and their parties) as having limited poll information that they use to adaptively choose positions many times during the course of a campaign. The candidates adapt or move using a search algorithm that provides a good approximation of the ways that candidates actually behave in a real election. Therefore, my results help to give a more accurate description of reality and help to make better predictions than previous (non-computational) spatial models can.
Introduction
Ever since Anthony Downs (1957), the spatial model of elections has made an important contribution to our understanding of the political process. It is a model that is appealing because it is both simple and descriptive, and its use is widespread in political science. The basic idea of the spatial model is that a voter has a ?position? or ideal point on one or more issues or dimensions, and the closer policy is to this ideal point, the better off the voter is. For example the amount she thinks should be spent on defense or her standing on a general left to right, liberal to conservative scale. Since it is generally assumed that candidates will implement whatever platform they run on, and there are generally only 2 candidates, the voter can simply vote for the candidate that is closest to her (in weighted Euclidean distance). In the one-dimensional case, voting for the closest candidate is a very simple task, and if all of the voters behave in this way, the result is the outcome described in Black?s(1958) median voter theorem. Namely, each candidate uses the platform that is the median voter?s ideal point, and whichever candidate the median voter votes for will win (it is generally assumed that a voter randomly votes for a candidate if she is indifferent). Note that if either candidate moves away from the median voter?s ideal point, the other candidate will get more than half of the vote (the median voter with certainty now, and every voter on the side of the median that the other candidate is not), and win with certainty. This result does not describe what we see empirically very well. In the real world, candidates do not run on identical platforms, they have distinct positions on at least some issues.
When the spatial model is expanded to multiple issue dimensions it seems much more realistic, however, things become much more complicated. If the voters assume candidates report their true intended policy during the campaign, or if there is some enforcement mechanism to ensure campaign promises are implemented, then the voter still has a simple task, vote for the nearest candidate. The job of the candidate however is now much more complicated. The problem is, as Plott (1967) shows, there is no stable best point, that is no point that can not be defeated by some other point, unless all of the voters are perfectly radically balanced, which is a probability zero event. Indeed, McKelvey (1973) shows that the smallest set of points such that no point outside the set beats any point inside the set (the top cycle set) is the entire space.
There are several solutions to this problem. One is to assume that this is really the way the world works, and whoever sets their position first will lose the election because their opponent can just run on one of the points that defeats their chosen point. However, this also does not mach empirical evidence. The other is to impose a very tight set of assumptions that can prevent this from happening by guaranteeing a stable global maximum point. As mentioned earlier, Plott shows the assumption required is to assume all of the voters perfectly radially balanced. However, since this is in general a probability zero event, and even a tiny shift by any 1 of the voters can destroy the symmetry, this seems very unrealistic as a representation of the real world.
Another major problem with this version of the spatial model is that it assumes that the candidates have complete information about the preferences of every voter. They need this information to ensure that they can find a point to beat their opponent. Obviously, real politicians do not know the exact position of every voter on every issue, they only have the more limited (and inexact) information they can gather through polls, focus groups, previous elections, and other such sources.
The model I propose to use to study elections does not suffer from these same problems. It is derived from a model developed by Kollman, Miller, and Page who I will refer to hereafter as KMP. In the KMP model, voters have an ideal position on each issue that is chosen from a finite set of possible issue positions. Since voters preferences are linear, and candidates vote maximize, this is so far exactly like Kramer?s Dynamical model. However, KMP add polls to the model. That is candidates can not automatically find a point that beats their opponent, instead they have a limited number of polls to try to find a better point
This model, and computational models in general, is also solved in a fundamentally different way. Instead of deriving a result and its properties, one is instead simulated computationally. This means that the model can be much more complicated and use more realistic assumptions, but still yield strong results and predictions. This computer simulation approach has been used widely in other fields of science, particularly in Physics and Biology, and is beginning to be used more in Political Science and Economics.
This type of computational modeling allows me to create a more realistic version of the spatial model. Instead of saying that candidates have full knowledge of voters positions or are uncertain about voter?s positions in some probabilistic way, I can model the candidates as having limited resources and information. This means that instead of seeing the true distribution of voters , or the true distribution through some uncertainty function, candidates see only the positions of voters that they have the time and the resources to poll. In my election model, candidates compete in a spatial framework where they poll voters to obtain information, and then adjust their position to try to win election. This dynamic process is repeated over many elections to search for consistent results. The voter?s job is still the same, they vote for whichever candidate is the closest to them. In the next section, I will define the model more exactly.