抄録
It is agreed that the application of spatial theory of competition to political theory of voting leads to a very fruitful analysis of the complex phenomena generated by the political enigma.
We should, however, note the need for critical evaluation of naive applications. D.E. Stockes critisizes the Downsian model of political spatial competition from the political point of view. He asserts that the performances of such model are subject to characteristic constraints of political dynamics.
We shall investigate more simple and exact but unsolvable problems than the above critical ones. First, we shall suggest that there is an ‘indeterministic character’ of spatial competitive equilibrium with the set of ‘tying issues’ preventing the process from ending. Second, we shall formulate the multi-issued decision model which can treat such a set of ‘tying issues’ with an application of a simple stochastic process.
From the calculation of our model, we find the following results:
1) The ‘tying issues’ do not have any influence on the competitive process. Therefore it is very rational that the candidates manage to change the ‘losable issues’ to be the ‘tying’ ones with some strategies.
2) The cumulated process is prevailing in the sequential contest, such that, the higher the score of ‘winning’, the greater the advantage to the competition. This proposition is equivalent to the following conjecture of O. Davis et al:
Candidates in strategically advantageous positions should increase the dimensionality of the contest while candidates in disadvantageous positions should simplify the election (i.e., reduce the dimensionality) in addition to shifting to a dominant position.
3) As the number of issues is increased, the ‘fair’ political contest remains fair, and counterintuitively, no ‘unfair’ contest can be changed into ‘fair’ one. As the number of exposed issues become infinitely large, the candidate or the party who posesses more advantageous characteristics, a priori, prevails in the process of political contest.
