The Theory of Political Coalitions

Last updated
The Theory of Political Coalitions
Author William H. Riker
Subject Political science
Publisher Yale University Press
Publication date
1962
OCLC 00325635

The Theory of Political Coalitions is an academic book on positive political theory written by the American political scientist William H. Riker and published in 1962. It uses game theory to formalize political theory. In it, Riker deduces the size principle. On its postulates, politicians are proved to form winning, minimal-size coalitions. [1] The work runs contrary to a previous theory by Anthony Downs that they try to maximize their respective votes. Riker supposes that attracting more votes requires resources and that politicians run to win. A rational politician tries to form a coalition that is as large as necessary to win but not larger. [2]

Contents

Use of Game Theory

Out of the varied models of game theory, Riker asserts that those involving the number of players are the most in understanding society [incomplete: the most ___ ?]. [3] In particular, Riker bases his primary examination and discussion of game theory to zero-sum situations involving three-or-more-person games (more easily known as n-player or, as Riker calls it, n-person games). He justifies this on the grounds that in n-person games the main activity of the players is to select not only strategies, but partners. Compared to one or two person games where maximum gain is the only thing sought, n-person games involve the potential for parallelism of interests. Conflict does exist, especially when the game is zero-sum, but there is now also an additional possibility for alliance and collusion. [4]

Riker points to two main concepts devised by John Von Neumann and Oscar Morgenstern as being an important limit on the potential coalitions in a n-person game. These are the characteristic function and the imputation concept. The characteristic function is the statement of the total payment to each coalition possible in the game. Riker points to it as significant as, when comparing the lists of payments to potential coalitions, the least profitable coalitions will not be considered by players. [5] The imputation concept refers to the specific list of payments to each player in a given structure of coalitions. The key thing Riker points out for this concept is that while there is generally a very large number of possible coalitions, only some of these possibilities will be considered by players due to some being more advantageous for the coalition members than others. The importance of this, Riker says, is that, "if one can put limitations on the ... imputations that will be seriously considered by the players, then one also puts limitations on the process of coalition making- inasmuch as imputations are related to particular partitions into coalitions." [6]

Size Principle and Minimal Size Coalitions

In his book Riker uses some notions from game theory to derive a fundamental principle concerning the size of coalitions. Specifically, he derived the following statement from the notions examined. "In n-person, zero sum games, where side-payments are permitted, where players are rational, and where they have perfect information, only minimum winning coalitions occur." [7] Riker builds on this to form a descriptive statement, or sociological law as he puts it, about the natural world which embodies his size principle. He states this as, "in social situations similar to n-person, zero-sum games with side-payments, participants create coalitions just as large as they believe will ensure winning and no larger." [7]

In a five-party system, if, after a general election, this representation is given:

Party AParty BParty CParty DParty E
Number of representatives54026254Sum: 100

Three winning coalitions are possible:

Party B and CParty B and DParty C and D
40+26=66 representatives40+25=65 representatives26+25=51 representatives

If it is now presumed that power will be divided according to strength within the coalition, the parties will prefer the largest relative size within the coalition. The result is that the coalition with C and D is the winning coalition. The largest party is thus kept from power.

Criticism

In his article, "On the Size of Winning Coalitions," Harvard University Professor Kenneth Sheplse asserted that "minimum winning coalitions constitute unstable equilibrium points in n-person zero-sum games". [8] This point extends analysis from Robert Butterworth's critique of Riker's size principle. [9] Sheplse's critique is that while "there appear to be forces in the coalition formation process that drive winning coalitions toward minimal size," [8] these forces are unable to keep the coalitions minimal. Sheplse argues that if "the usual assumptions about n-person zero-sum coalition processes are supplemented with assumptions about coalition intentions and capabilities, there are good reasons to expect minimum winning coalitions in all but the most extreme instances." [8]

More general criticism of Riker's size principle has been based on the vagueness of its predictive ability, especially when information is not perfect. Eric Browne, in his article, "Testing Theories of Coalition Formation in the European Context," argues this point. [10] He says that it can be demonstrated that no uniquely favoured proto-coalition (a player who, when in a coalition, makes said coalition more valuable than any other) is produced by the size principle. He therefore argues that Riker's theory results in a position of not being able to make a definitive prediction. He expresses this further by saying. "All we may state is that, of the four possible winning coalitions, one of the three two-party coalitions will form." [10] Additionally, Browne points to the knowledge aspect of Riker's theory as posing a problem. He argues that while the context of governing coalitions "minimizes the problem of perfect information" (meaning that parties know how possible coalitions will benefit them), leaders may not be able to "depend on their parties to vote with perfect cohesion. If they have reason to expect that they will not, we might then expect that greater than minimal winning coalitions will form." [10]

Other criticisms of the size principle have been directed at the validity of its proof [11] and the assumption "that politicians are primarily driven by the intrinsic benefits of office and that they will coalesce with any party out of expediency." [12]

Related Research Articles

Game theory is the study of mathematical models of strategic interactions among rational agents. It has applications in many fields of social science, used extensively in economics as well as in logic, systems science and computer science. Traditional game theory addressed two-person zero-sum games, in which a participant's gains or losses are exactly balanced by the losses and gains of the other participant. In the 21st century, game theory applies to a wider range of behavioral relations, and it is now an umbrella term for the science of rational decision making in humans, animals, as well as computers.

Logrolling is the trading of favors, or quid pro quo, such as vote trading by legislative members to obtain passage of actions of interest to each legislative member. In organizational analysis, it refers to a practice in which different organizations promote each other's agendas, each in the expectation that the other will reciprocate. In an academic context, the Nuttall Encyclopedia describes logrolling as "mutual praise by authors of each other's work". Where intricate tactics or strategy are involved, the process may be called horse trading.

Minmax is a decision rule used in artificial intelligence, decision theory, game theory, statistics, and philosophy for minimizing the possible loss for a worst case scenario. When dealing with gains, it is referred to as "maximin" – to maximize the minimum gain. Originally formulated for several-player zero-sum game theory, covering both the cases where players take alternate moves and those where they make simultaneous moves, it has also been extended to more complex games and to general decision-making in the presence of uncertainty.

<span class="mw-page-title-main">Nim</span> Game of strategy

Nim is a mathematical game of strategy in which two players take turns removing objects from distinct heaps or piles. On each turn, a player must remove at least one object, and may remove any number of objects provided they all come from the same heap or pile. Depending on the version being played, the goal of the game is either to avoid taking the last object or to take the last object.

Zero-sum game is a mathematical representation in game theory and economic theory of a situation that involves two sides, where the result is an advantage for one side and an equivalent loss for the other. In other words, player one's gain is equivalent to player two's loss, with the result that the net improvement in benefit of the game is zero.

William Harrison Riker was an American political scientist who is prominent for applying game theory and mathematics to political science. He helped to establish University of Rochester as a center of behavioral revolution in political science.

In game theory, the Nash equilibrium, named after the mathematician John Nash, is the most common way to define the solution of a non-cooperative game involving two or more players. In a Nash equilibrium, each player is assumed to know the equilibrium strategies of the other players, and no one has anything to gain by changing only one's own strategy. The principle of Nash equilibrium dates back to the time of Cournot, who in 1838 applied it to competing firms choosing outputs.

<span class="mw-page-title-main">Shapley value</span> Concept in game theory

The Shapley value is a solution concept in cooperative game theory. It was named in honor of Lloyd Shapley, who introduced it in 1951 and won the Nobel Memorial Prize in Economic Sciences for it in 2012. To each cooperative game it assigns a unique distribution of a total surplus generated by the coalition of all players. The Shapley value is characterized by a collection of desirable properties. Hart (1989) provides a survey of the subject.

In game theory, a cooperative game is a game with competition between groups of players ("coalitions") due to the possibility of external enforcement of cooperative behavior. Those are opposed to non-cooperative games in which there is either no possibility to forge alliances or all agreements need to be self-enforcing.

Game theory is the branch of mathematics in which games are studied: that is, models describing human behaviour. This is a glossary of some terms of the subject.

In cooperative game theory, the core is the set of feasible allocations or imputations where no coalition of agents can benefit by breaking away from the grand coalition. One can think of the core corresponding to situations where it is possible to sustain cooperation among all agents. A coalition is said to improve upon or block a feasible allocation if the members of that coalition can generate more value among themselves than they are allocated in the original allocation. As such, that coalition is not incentivized to stay with the grand coalition.

<span class="mw-page-title-main">Melvin Dresher</span> Polish-American mathematician (1911-1992)

Melvin Dresher was a Polish-born American mathematician, notable for developing, with Merrill Flood, the game theoretical model of cooperation and conflict known as the Prisoner's dilemma while at RAND in 1950.

William Anthony Gamson was a professor of Sociology at Boston College, where he was also the co-director of the Media Research and Action Project (MRAP). He is the author of numerous books and articles on political discourse, the mass-media and social movements from as early as the 1960s. His influential works include Power and Discontent (1968), The Strategy of Social Protest (1975), Encounters with Unjust Authority (1982) and Talking Politics (2002), as well as numerous editions of SIMSOC.

In fully cooperative games players will opt to form coalitions when the value of the payoff is equal to or greater than if they were to work alone. The focus of the game is to find acceptable distributions of the payoff of the grand coalition. Distributions where a player receives less than it could obtain on its own, without cooperating with anyone else, are unacceptable - a condition known as individual rationality. Imputations are distributions that are efficient and are individually rational.

Game theory has been used as a tool for modeling and studying interactions between cognitive radios envisioned to operate in future communications systems. Such terminals will have the capability to adapt to the context they operate in, through possibly power and rate control as well as channel selection. Software agents embedded in these terminals will potentially be selfish, meaning they will only try to maximize the throughput/connectivity of the terminal they function for, as opposed to maximizing the welfare of the system they operate in. Thus, the potential interactions among them can be modeled through non-cooperative games. The researchers in this field often strive to determine the stable operating points of systems composed of such selfish terminals, and try to come up with a minimum set of rules (etiquette) so as to make sure that the optimality loss compared to a cooperative – centrally controlled setting – is kept at a minimum.

In game theory, a strictly determined game is a two-player zero-sum game that has at least one Nash equilibrium with both players using pure strategies. The value of a strictly determined game is equal to the value of the equilibrium outcome. Most finite combinatorial games, like tic-tac-toe, chess, draughts, and go, are strictly determined games.

In algorithmic game theory, a succinct game or a succinctly representable game is a game which may be represented in a size much smaller than its normal form representation. Without placing constraints on player utilities, describing a game of players, each facing strategies, requires listing utility values. Even trivial algorithms are capable of finding a Nash equilibrium in a time polynomial in the length of such a large input. A succinct game is of polynomial type if in a game represented by a string of length n the number of players, as well as the number of strategies of each player, is bounded by a polynomial in n.

<span class="mw-page-title-main">Jean-François Mertens</span> Belgian game theorist (1946–2012)

Jean-François Mertens was a Belgian game theorist and mathematical economist.

Heresthetic is an approach to understanding how political actors manipulate the decision-making process so they can win. Heresthetic is a positive political theory, including aspects of game theory, public choice theory, rational choice theory, and social choice theory to political science. Political scientist William H. Riker is considered the creator and one of the most prominent supports of theory.

In cooperative game theory, the nucleolus of a cooperative game is the solution that maximizes the smallest excess of a coalition. Subject to that, the nucleolus satisfies the second-smallest excess; and so on, in the leximin order. The nucleolus was introduced by David Schmeidler.

References

  1. ↑ Fagen, R. (1963). The Theory of Political Coalitions. By William H. Riker. (New Haven: Yale University Press, 1962. Pp . x, 292. $6.00.). American Political Science Review,57(2), 446-447. doi:10.2307/1952835
  2. ↑ RIker, William (1962). The Theory of Political Coalitions . New Haven and London: Yale University. pp.  33.
  3. ↑ Riker, William (1962). The Theory of Political Coalitions . New Haven and London: Yale University. pp.  34.
  4. ↑ Riker, William (1962). The Theory of Political Coalitions . New Haven and London: Yale University Press. pp.  35.
  5. ↑ Riker, William (1962). The Theory of Political Coalitions . New Haven and London: Yale University Press. pp.  36.
  6. ↑ Riker, William (1962). The Theory of Political Coalitions . New Haven and London: Yale University Press. pp.  37.
  7. 1 2 Riker, William (1962). The Theory of Political Coalitions . New Haven and London: Yale University Press. pp.  32.
  8. 1 2 3 Sheplse, Kenneth (June 1974). "On the Size of Winning Coalitions". The American Political Science Review. 68 (2): 519–521. doi:10.2307/1959499. JSTOR   1959499. S2CID   146967147.
  9. ↑ Butterworth, Robert (June 1974). "Comment on Sheplse's "on the Size of Winning Coalitions"". The American Political Science Review. 68 (2): 519–521. doi:10.2307/1959500. JSTOR   1959500. S2CID   147261584.
  10. 1 2 3 Browne, Eric (1971). "Testing Theories of Coalition Formation in the European Context". Comparative Politics. 3 (4): 391–421. doi:10.1177/001041407100300401. S2CID   152692714.
  11. ↑ Hardin, Russell (December 1976). "Hollow Victory: Minimum Winning Coalition". The American Political Science Review. 70 (4): 1202–1214. doi:10.2307/1959385. JSTOR   1959385. S2CID   146833460.
  12. ↑ Boston, Johnathan (June 2011). "Government Formation in New Zealand under MMP: Theory and practice". Political Science. 63: 79–105. doi:10.1177/0032318711406879. S2CID   154652895.
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.