An Influence of Voters' Preferences on the Stable Parliamentary Seat Share

In this paper, we show that the dynamics of a parliament seat share using an adoptive process modeled by urn scheme. In particular, we clarify the condition under which one dominant party or co-existence arises, when voters recognize the political effectiveness as important. One of the important factors for voters to decide their voting is how a political party's proposal is close to their ideal, which reflects their religion, social class, age and so on. There exists another important factor to choose a party. In the literature it is often supposed that the winning party has the power to implement any proposal with probability 1. However, voters have room to consider the likelihood that a party will implement its proposal, i.e., the political effectiveness. Some of voters may be more in favor of the policy that was announced by the defeated party; others, on the contrary, may be in favor of the winning party's proposal. The actions taken by the government are influenced by voters. The influence of voters in favor of a proposal will become bigger if the proportion of seats obtained by the corresponding party. Clearly a party winning 51% of the seats will have more difficulty to carry out its proposal than one winning 80% of the seats. As show in Duverger(1967), voters for small parties will see that their vote is being `wasted' and they will switch to supporting a major party. We consider the case where voters pay attention to two points to choose a party; the closeness between a party's ideology and own ideal, and the political effectiveness. Here, we consider the simple society where there are two parties, say, X and Y, and three type voters, say, x, y, and z. Voter x receives positive benefit from X and negative one from Y. She always votes for party X tough X has any low seat share. Conversely, voter y obtains negative benefit from X and positive one from Y. He votes for party Y irrespective of the seat share of Y. Voter z gets the same benefits from both parties. Party X and Y are indifferent for voter z. Voter z votes for a party with higher seat share. Voter x and y count the closeness to a party strongly and they ignore the political effectiveness. Voter x has the low critical seat share to vote for party X and voter y has the high critical seat share to vote for X. Voter z pays attention to the political effectiveness. He has the moderate critical seat share to vote for party X. We regard a voter's critical seat share as a voter's preference. For purposes of comparison we consider two shapes of distribution of voters' preferences, bimodal and single-peaked. If voters' preferences are distributed as bimodal, each party has strong supporters who always vote for the support party and the proportion of voters who care the political effectiveness as important is small. As each party has strong supports potentially even if it leaves what initial state, in progress of time, two seat shares become equivalent, i.e., the long term co-existence is realized in the equilibrium. Conversely, if voters' preferences are distributed as single-peaked, most voters are interested in the political effectiveness. Then, a party with higher seat share is more attractive for voters and it gains an even higher seat share. After all, a party with a high initial seat share comes into power, i.e., the lock-in into one of political party is realized. The dynamics treated in this paper is the generalized urn process discussed in Hill et al. (1980), Arthur et al. (1983), and Dosi et al. (1994). As Dosi et al. (1994) mentioned, by specifying the function which characterizes an agent's behavior, it is possible to analyze the stochastic evolution of the share. We define the voters' behavioral patterns and demonstrate how the global forces ruling the dynamics of whole populations can be derived from the individual behavior of voters