The Theory of Political Coalitions by William H. Riker

Maintaining a coalition is expensive as it requires payments from the head to the other members (cf. patronage). These costs incent the formation of "minimal winning coalitions", thereby creating losers.

For empires, this means that any established empire has a number of disaffected who can be turned against the empire when a new power arises. This potential fifth column needs to be rewarded even in loss, eg. public goods or direct incentives, to prevent their realignment and the formation of new winning coalition.

The more general purpose of this book is to add another (putative) example (to the several that already exist) of the fact that it is or may be possible for political science to rise above the level of wisdom literature and indeed to join economics and psychology in the creation of genuine sciences of human behavior. There is considerable intel lectual ferment among political scientists today owing to the fact that the traditional methods of their discipline seem to have wound up in a cul-de-sac. These traditional methods-i.e., history writing, the description of institu tions, and legal analysis-have been thoroughly exploited in the last two generations and now it seems to many (in cluding myself) that they can produce only wisdom and neither science nor knowledge. And while wisdom is cer tainly useful in the af f airs of men, such a result is a failure to live up to the promise in the name political science.
Recently David Easton has of f ered a def i ni tion that combines all these and, besides, fi ts politics into the general scheme of the social sciences. Politics, he said, is the authoritative allocation of value. By emphasizing allocation, which is a kind of action, he made it clear that politics is social behavior, a study of dynamics and not pri marily a study of such static things as forms of government.

Thereby he fit political science into the tradition that selects motion and action as the proper concern of science, a tradition that has increasingly dominated Western scien tif i c thought for the past century and a half. Furthermore, since the usual def i nition of economics is "the allocation of scarce resources," he showed both the parallelism and divergence of the two kinds of activity by the parallelism and divergence of the def i nitions.

John Von Neumann and Oskar Morgenstern, The Theory of Games and Economic Behavior (Princeton, Princeton University Press, 1944; I , hereafter cite the second edition 1947). For the discovery by political scientists of the relevance of game theory to their concerns see Martin Shubik, ed., Readings in Game Theor y and Political Behavior (Garden City, Doubleday, 1954); Richard Snyder, "Game Theory and the Analysis of Political Behavior," in Stephen K. Bailey et al., Research Frontiers in Politics and Government (Washington, The Brookings Institution, 1955);

Herbert A. Simon, Models of Man (New York, John Wiley, 1957), especially the introduction; Morton A. Kaplan, System and Pror ; ess in Interna-tional Politics (New York, John Wiley, 1957), pp. 223 ff .; James Buchanan and Gordon Tullock, The Calculus of Consent (Ann Arbor, University of Michigan Press, 1962), passim.

a fi ve-person parlor game in which the object of the players is to form a winning coalition to take an amount of money specif i ed in the course of the play away from the losers. In brief outline this game, called Talleyrand, consists of the fol lowing rules: 2 I . There are fi ve players whose object is to form a winning coalition of three or more players to take money from the losers.

2. The fi rst player, chosen by chance, proposes to take an amount, a1, from each loser and at the same time passes notes of f ering amounts, b1,2, b1,3, b1,4, b1,5, to other players to join him in the coalition (the fi rst number of the subscript of b refers to the of f ering player; the second to the receiving player). By making of f ers, he becomes a "leader." The second player in a clockwise direction re sponds by (1) accepting l's of f er by passing a note of acceptance, or (2) leading a new coalition in the manner just described for player 1, or (3) acting as if he were a leader when in fact he is accepting l 's of f er. Players 3, 4, and 5 have the same options with respect to of f ers as do players 1 and 2. All of f ers are for one full round of moves uncondi tionally binding on the leader if and only if the coalition actually forms during that round; but ac ceptances are not binding on the accepting players.

3. Once each player has had a move of this sort, the fi rst player has the option of announcing a coali tion. If the members of his coalition agree that it exists, then the announcer collects a1 from each loser and pays bw bw etc. If the members do not agree, I forfeits the amount a1 to the pot where it may subsequently be claimed by the leader of the winning coalition. After this forfeiture, I may move in the fashion described for player 2 in para graph 2 above. During the second and third rounds of moves each leader has the option of announcing a winning coalition if he chooses, collecting a, and paying b,1 if it forms and forfeiting a, if it does not.

4. A hand consists of at most three rounds of m.oves.

If no winning coalition has been formed in a hand, all leaders must forfeit to the pot the amounts a, and the money in the pot remains for the next hand of the game. In the second hand, player 2 must start the play; in the third hand, player 3; etc

So it may be said that when Jackson took of f i ce in 1 829, he had command of a rela tively valueless coalition to which nearly everybody claimed to belong. This is the situation Tocqueville de scribed when he said that the "great parties" (i.e. Federal ist and Republican) had been replaced with "minor parties." 3 But at the very time Tocqueville observed this, Jackson was engaged in reshaping his grand coalition into a mini mal winning one. While of course he could not carry through the kind of analysis undertaken here, still he could and did sense that nothing could be achieved with out a loyal and devoted set of allies. And it turned out in practice that the only way he could obtain these was by expelling some lukewarm friends from the grand coali tion.
He shared with Washington, it is true, a pride in playing the role of Cincinnatus; but he also modeled himself on the great Whig lords. From the time of the battle of New Or leans, Jackson knew he was the chief man in the West, the magnate of the frontier, its greatest landowner, its greatest horse breeder, its greatest captain, its greatest representa tive. Thus occurred this curious combination: a man of the people with a sense of honor as delicate as a Tuscan count's. And it is exactly this combination of qualities that Jackson used to minimize his winning coalition. What Jackson asked of the people in his coalition was not pri marily that they agree on a particular policy (although he asked that often enough) but rather that they ag r ee with him.
It had been an overwhelming majority in the fi fties and would quite probably still be at least winning in 1 868, if it could be re-activated. What, specif i cally, Stevens and Sumner feared was that the now solidily Democratic border and Southern states might re-ally with the Democracy of New York, Pennsylvania, and the northern Middle West. If this hap pened, the Republicans were sure to lose. Hence followed the Stevens and Sumner plan of military reconstruction which was intended to and actually did transform the South from Democratic to Republican, thereby guaran teeing Republican victory in the whole nation. The tech nique of this plan was to forbid re-entry of Southern states into the union until it had been made certain that they would vote Republican-made certain, that is, by organi zation of Negro voters and disfranchisement of white voters (both under the supervision of a Republican army).

Thus, by appropriate inclusion and exclusion of players, the Republicans made a new n-person game in which their coalition was assured of overwhelming victory. Their victory was in fact so overwhelming that in 1872 the Dem ocratic party did not even feel capable of of f ering a candi date for the Presidency.

The customary def i nition of total war includes two features: (I) war such that the object is the complete de struction of the government(s) on the losing side and (2) war such that all great powers in the system participate.

This is a behavioral version of the zero-sum condition in a simple game. The game is simple because all the losing players--which are governments even though they may claim to be mere agents for the people they govern-lose their existence, presumably the worst loss they could sus tain individually. It is zero-sum because precisely the loss of the losers, i.e., their destruction, is the announced ob ject of the winners. The gain is the exact reverse of the loss. Furthermore, the zero-sum condition in an n-person game involves the notion of complementary coalitions and this notion is roughly represented by the second part of the def i nition of total war.

Total war has further this interesting feature: If one side actually wins, that is, if one side is exhausted before the other, then victory, by removing the losers, transforms a (probably minimal) winning coalition into a grand coali tion. And, if we accept characteristic function theory, grand coalitions are worthless.

The anti Axis coalition of the United States, United Kingdom, and Soviet Union was uneasy enough to begin with owing to the bitter ideological dif f erences between the two former and the latter. Not unreasonably, therefore, this uneasy coalition of the whole did not long survive the victories which rendered it grand. Having defeated the Axis, the winners had nothing to win from unless they split up and tried to win from each other. At Yalta, even at Potsdam, the heads of the thre< ' : victorious governments planned a continuation of their wartime alliance under the very name they had used to fi ght the war, i.e., the United Na tions. But within less than a year after Potsdam, indeed even before it occurred, the United States and the Soviet Union were scrambling about the world to gain the alle giance of the uncommitted nations to one of the two hos tile coalitions they were forming. And at the time of the Korean episode the United Nations itself came to be re gard! ed by the Soviet Union as part of the United States' network of alliances.
From these three instances of the end product of total war one can readily conclude: the winning coalitions of total war do not long survive victory. Both in the model and in actuality they have become valueless.
This debate, which often arises journalistically, concerns whether or not there is a discernible ideological dif f erence between the parties. In particular elections there are in disputable dif f erences, of course, if only the dif f erences in the character of the candidates. But in several elections, especially several simultaneous elections but also even in elections over time, it may well be that no discernible dif ference exists. Lord Bryce once quoted with approval a journalist's observation that the parties in America were like two bottles with dif f erent labels but both empty.
The most direct statement of the irreconcilability of these two positions is found in Downs' work, An Economic Theory of Democracy. For him the problem arises thus.

His model is based on two axioms: (1) that all citizens are rational in the sense that they seek to maximize utility from governmental actions and (2) that parties are rational in the sense that they seek to maximize votes. He then imagines a situation in which citizens, taken together, have diverse interests and in which two parties are each allowed to appeal to as many interests as they wish in order to maximize membership. As a consequence, in this situation there is a tremendous overlapping of the policies of the two parties (and, as he points out, the overlap is even greater when there are more than two parties). Of this sit uation he remarks: "Clearly both parties are trying to be as ambiguous as possible."

A much easier and much less discommoding way to re solve it is the second alternative, that is to change the def i nition of rationality. Instead of simply asserting that par ties seek to maximize votes, one could assert instead the size principle: that parties seek to increase votes only up to the size of a minimum winning coalition. If the axiom is revised in this way, parties no longer have an incentive toward absolute ambiguity. Including the information ef fect in the axiom makes the resolution even easier. Then parties have an incentive to becloud issues only in the case of issues that are of concern to the voters about whom they have imperfect information.
The cautious realism with which the mystic Gandhi used the political technique of the fast is a case in point. All his fasts of course brought his charisma into play for they depended for success on the fact that the per sons whom he sought to inf l uence dared not allow a saint to die. It is instructive to note, theref o re, that the vast majority of his fasts were directed against caste Hindus, that is, they could be ended only if Hindus either performed some action he desired or desisted from some action he disapproved. Caste Hindus were, of course, those persons most likely to be convinced of his saintliness and therefore the persons most likely to feel the force of this weapon. Some of his fasts were even directed against persons in his in ; t mediate entourage. Only four of his fasts were directed against the B.ritish, although these are the ones most widely publicized.

And these four, it should be observed, were undertaken when all of Hindu India was af l ame and when the British were for one reason or another compelled by political circumstances to show greater-than-usual deference to Indian and world public opinion. The inference I draw from a survey of Gandhi's political fasting is that, with a realism somewhat un expected in a mystic, he fasted only when he could win. Never once did he expose his charisma to the humiliation of abandoning a fast in failure.

Assuming that, as the Democratic dominance developed from the 1 870s and 1 880s on to the present, the appropriate model of politics in those states without traditional Republican minorities was that set forth in Chapters 5 and 6, then our present question is: Why have some state Democratic parties some time developed a two-faction system and why have others not done so? The fundamental element of the answer is, of course, the fact that a peculiar double sort oJE game is played there: One is a game for control of society as a whole; the other is a game for control of the government. In the former and more important game the key feature is the fact that Negroes have been excluded entirely from the political system. That is, by means of a S) I Stematic and almost complete agreement among whites, Negroes are excluded from participation in the game for control of government. The exigencies of the game for control of society, which most Southern politicians regard as the more important, are what determine the structural features of the game for control of government. What is absolutely essential in the latter game is that, if any actors are eliminated (i.e., if any become more or less permanent lo.)ers in a two-faction system), they must not ally with Negroes to upset the white victory in the game for control of society. Hence the players in the game for control of government have their own unwritten version of Kaplan's third rule, to wit, that no faction may be allowed to be a quasi-permanent loser if there is any likelihood that it will attempt to escape this position by bringing Negroes imo the political system. In most of the state parties most of the time since the 1890s, this rule has in practice meant that no issue may be raised that is so divisive in the white society that two permanent factions may be built around it. Occasionally agrarian radicals have evaded this rule and actually created a two-faction system in the game for the control of government (e.g., Tillman, Talmadge, Long, et al.), but in almost every instance they have done so only by identifying themselves as the most virulent of Negro-haters. ...

The only agrarian radicals in a two-faction Southern Democratic party who have not also been white supremacy extremists were the Longs of Louisiana. It seems likely that they were able to operate without giving this assur ance chief l y because white supremacy was so well estab lished that no one suspected that they might coalesce with Negroes.

In the nineteenth-century European balance, all rulers feared the spread of repub lican ideas. The ghost of Robespierre haunted every Euro pean privy council, frightening them into a certain mod eration. But particular ghosts are forgotten, especially when rationalist devotees of real-politik become privy councilors. So one might say that Bismarck exorcized the ghost of Robespierre and thus removed the moral restraint maintaining the balance.
The intent behind all changes of the rules of membership is, of course, to se cure the quasi-permanent ascendancy of a temporarily ascendant coalition. That is, a coalition that is momen tarily winning hopes that it may prolong its winning through future decisions by means of the support of new members who will presumably be grateful for admission to those who admitted them. Or, in the opposite maneu ver, a coalition that is momentarily winning hopes that it may prolong its winning by expelling members of the losing side so that the losers will not be strong enough to win even if they should be able to seduce a part of the winning coalition. The expansion of the electorate in all democratic countries has almost always been occasioned by transparent motives of this sort. In the case of the United States, for example, the relaxation of property qualif i cations for voting were maneuvers by Jef f ersonian Democrats (or the radical wing of that party) to defeat Federalists or conservative Democrats; the Fifteenth Amendment was a maneuver by Republicans to defeat Democrats by obtaining Negro votes, and the Nineteenth Amendment was a maneuver by reformers to def eat po litical bosses (on the theory that women would be more hostile than men to political corruption).2 Or in the case of the fi rst consciously democratic system, the reforms of Cleisthenes in Athens were a maneuver to grant citizen ship to persons who would support the radical party that was ultimately led by Pericles.3
The possibility of disequilibrium owing to miscalcula tion in side-payments is enormously increased if one takes into consideration not only payments to followers, but payments to leaders themselves. Necessarily the leaders' share of winnings on any decision must be a part of the total. calculation. Hence, a theoretical analysis of a system or body cannot leave out the leaders' share.

The list in Chapter ti of payments to followers does not fully describe the payments to leaders. Of course, leaders do receive some of the same kinds of payments, e.g., valu able objects, changes in the content of policy, support on subsequent coalitions, etc. But leaders are not ordinarily subj ect to the threat of reprisal nor can they experience the emotional satisfaction of following. Instead they re ceive at least. the following kinds of additional rewards:

I. The satisfactions of power: One can imagine at least two general types of motives for desiring power, which I def i ne, following Dahl, as the ability to make someone else do something he would not otherwise do.

The satisfactions of prestige: While leaders cannot experience the emotional satisfaction of following, they can, perhaps, experience a complementary satisfaction of being followed.

The satisfactions of continuation: The leader who has never paid followers with emotional satisfaction or threats of reprisal need not fear the loss of his role.

The signif i cance of the existence of these three types of special payments to leaders is twofold. In the fi rst place, it encourages the development of opportunistic leaders. None of these three rewards can be paid out of contingent prof i ts in the decision itself. The payment here lies in winning, not in what is won.

Thus, in the last three centuries, scholars have produced a plethora of contrived explanations of the decline of em pires . Some have explained the events in terms of a (usm:Jly mystical) dissipation of the will to win (e.g. Gib bon, Spengler, Toynbee). Others have explained them in terms of some (equally mystical) death and rebirth process in disguised and probably unconscious analogy to animal life e.g. Hegel and Marx). Still others, especially those in the Christian tradition, have explained in terms of un resolved conf l icts in the human psyche (e.g. Niebuhr) or more simply still in terms of divine retribution and test ing (e.g. Berdyaev).
explanation of the decline of empires and great coalitions. One is the size principle itself and the other is the tendency, men tioned in the last chapter, for leaders to miscalculate side payments and to pay more for winning than winning is "objectively" worth. By reason of the size principle, lead ers with the certain assurance of winning may actually expel some "minor" members whose interests conf l ict with the interests of some "major" members of the coalition. Even without expulsions, however, such leaders may re duce the size of their coalition simply by neglecting the interests of some members until the neglected ones defect to the other side. By such processes of expulsion and neglect, world-dominating empires can be expected to pare of f their excess weight, even to the point at which they are barely capable of winning. At this point the dan ger of overpayment for victory becomes great indeed.
The decline of Germany and Austria-Hungary is explicable enough by the fact that they lost two major decisions involving dis memberment as a penalty for loss. The decline of Eng land and France, however, is not so easily explained.

Were not these the winners? Should not their empires have fl ourished in victory? But they did not fl ourish. One can only conclude that, in the exigencies of conf l ict, they paid more for winning than winning was objectively worth. In the decadence of these nations, in the fact that even their cultural and intellectual leadership has passed to other peoples, one can see the results of overpayment.

the decline of every one of Toynbee's twenty-three past civilizations, as well as the decline of empires within the four existent ones, is fully explicable in terms of the size principle and overpayment to allies and followers, espe cially by means of military expenditures on Pyrrhic vic tories. In short, one can explain all declines of empires in terms of bad management rather than in terms of such mystical categories as a loss of will or a drive toward death or divine intervention.
Finally, resignation of leadership would involve the systematic betrayal of many peoples who have believed in us. A foretaste of what might happen can be observed in the results of the abortive Hungarian revolution of 1956. That revolution, which was partly predicated on an expectation of American aid, resulted in the slaughter of a large number of people, especially of idealistic and trusting adolescents. They did not understand that the foreign policy of "liberation" was announced by Secretary Dulles mostly for domestic consumption as an incident for the struggle for votes in the era of McCarthyism.
The second previously listed feature of the Age of Maneuver is a putative intensif i cation of the tone of politics.

It may seem to some who have lived through the recurrent crises of the Cold War in the Age of Equalization that the sense of crisis cannot be deepened. Yet, I suggest, exactly such deepening will occur. In the similar phases of equali zation and maneuver in American politics of the last cen tury and three-quarters the atmosphere of politics has been much more heated in ages of maneuver than in ages of equalization. The ages of maneuver have been those in which the two parties are approximately equal in voting strength, namely, the late 1790s, the 1 840s, the late 1870s and the 1 880s, the late 1930s and early 1940s and, possibly, the period we are entering now. Assuming that the partici pation of a large proportion of eligible voters is evidence of an intensity of emotion in politics, then the ages of ma neuver are also the ages of greatest intensity of emotion.

The proportion of eligible voters participating was at a high point for a generation on either side in the Presi dential elections of 1 840, 1 888, and 1 940. While we have no adequate record of voting in the 1 790s, it seems likely from scattered evidence that the turnout in the election of 1 800 was exceptionally high for its era. Even without the evidence from the amount of voting, however, there is much evidence that political life in the ages of maneuver was more vituperative than at other times. And excessive vituperation seems to me evidence of intensity of emotion.

In the age of Jef f erson the pattern of extreme vituperation was established by such journalists as Freneau, Bache, and Cobbett. It . was revived in Jackson's day by Isaac Hill, Duf f Green, and Nicholas Biddle. In the 1870s and 1 880s one kind of vituperation was so common it acquired a special name, "waving ; the bloody shirt." And those who remember the late 1930s know well the vituperative emo tions aroused by Franklin Roosevelt.