Abstract
This paper uses a forward-looking two-period coalitional game to analyze party prominent figures’ internal competition for personal power in the party and external cooperation on national elections for the party. Incorporating the electorate’s preference for new alternatives over the establishment, it characterizes the equilibrium of prominent figures’ (1) maneuver for personal power in the party; (2) grouping to form factions in the party or split-off new parties; (3) campaign effort in the national election for the party; and (4) the resulting outcomes of the national election. It shows that the electorate’s longing for new alternatives induces prominent figures to maneuver more in the party; form a new party instead of a faction; and campaign harder for the national election. This study synthesizes the analysis of internal party politics and inter-party competition.
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Notes
Prominent figures refer to those party members whose assertion and action can directly affect the party’s policies, decisions, and payoffs.
The term maneuver summarizes possible actions that promote one’s status in the party. For example, building alliances through interest exchange or common goals; competing for administrative positions, soliciting support through social events.
For this reason, we write \(p(m_{i}; m_{-i})\) as \(p(m_{i})\) when there is no potential confusion.
As will become clear in the following analysis, the Nash equilibrium of maneuver exists. The set of maneuver levels \(M_{i}\) is non-empty and convex; and given all others’ maneuver, a figure’s power \(p_{i}\) is continuous and quasi-concave on \(M_{i}\). Applying Proposition 20.3 of Osborne and Rubinstein (1994) we know the Nash equilibrium of the first period simultaneous maneuver exists. Moreover, with the synergy effect of grouping, the relative powers of all groups still sum to 1. We only need to define
$$\begin{aligned} P^{S*}= \frac{P^{S}}{\sum _{G\in \mathcal {J}} P^{G}}, \end{aligned}$$where \(\mathcal {J}\) is the partition of party J in which group G is an element. With this scaling, the power of each group is still increasing in all its members’ maneuver; and the relative power of each member in a group still increases with his maneuver.
Since all parties campaign simultaneously, each party can only deduce all other parties’ campaign effort and gives its best response; no party can wait to see others’ aggregate effort and revise its own accordingly. For this reason we write \(q(E^{J})\) instead of \(q(E^{J}; E^{-J})\) for the sake of brevity where there is no potential confusion. Moreover, we do not need to worry that the sum of each party’s probability of winning the election as a function of the total campaign effort chosen by its members may not sum to 1. We can simply define
$$\begin{aligned} q^{*}(E^{J})\equiv \frac{q(E^{J})}{\sum _{K\in T} q(E^{K})}, \end{aligned}$$with T the total number of parties in the second period. With this scaling, each party’s winning probability is still increasing in its total campaign effort. The existence of the Nash equilibrium of the second-period election competition is assured by similar reasoning as that for the Nash equilibrium of the first-period maneuver for personal power.
Since each figure’s campaign effort is determined by his already fixed status in his party and all parties campaign simultaneously, no party or figure has the chance to observe others’ campaign effort and then revise its or his campaign effort accordingly. Each figure can only deduce what other figures’ equilibrium behavior would be and give his best response. And his best response campaign effort is the extension of his best response maneuver to his fellow figures’ maneuver over the first period. This is because forward-looking figures take into account their future campaign effort while determining their maneuver and grouping in the party. Compounded with their corresponding campaign effort in the second period, the best response maneuver and grouping maximizes a figure’s aggregate payoff over the two periods. With or without prominent figures’ grouping, the Nash equilibrium of campaign competition exists. A party’s campaign effort is a compact convex set. Given all other parties’ campaign effort, a party’s winning probability and thus payoff is quasi-concave in its members’ aggregate campaign effort. Applying Kakutani fixed point as in p. 20 of Osborne and Rubinstein (1994), we are assured of the equilibrium of campaign effort.
Factions based on ideology or organizers’ personal charisma can also have quite uneven distribution of total power and gain. Here we focus on the strategic alliance based on pure interest calculation. Each prominent figure aims to obtain a larger share of party resources and attain the chance to become the party nominee for the national election.
When a new party is formed, it solicits pledged resources from donors. If it manages to win the national election, the attainable resources multiply.
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The author is grateful for referees and editors for reading each version of the paper with fresh and rigorous eyes. Their comments help generate a much better paper. One of the referees’ insightful and detailed suggestions are especially helpful. This paper also greatly benefits from the discussions of Xiao Luo, Eric Maskin, and Guoqiang Tian along various stages of its development. Equally sincerely, hope this paper provides an answer to Jin-See Wong’s question: “Why does a political party often not nominate the most intelligent and public-minded member as its candidate for national elections?”.
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Ueng, SF. Campaigning internally or externally. Ann Oper Res 301, 245–267 (2021). https://doi.org/10.1007/s10479-020-03815-1
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DOI: https://doi.org/10.1007/s10479-020-03815-1