¹ The research reported on in this article was conducted under the auspices of a Fulbright Fellowship, 1965–67. The material gathered in the course of this research has also been used in “Coalition Government in Japan,” Transactions of the Asiatic Society of Japan (forthcoming), “Jiminto to wa, Renritsu Seiken to Mitsuketari,” Chuo Koron (08, 1967)Google Scholar, and “Coalition Politics in One-Party Japan,” The Study of Coalition Behavior, Groennings, S., Kelley, W. E., and Leiserson, M. (eds.) (Holt-Rinehart-Winston, forthcoming)Google Scholar.

² “National Assembly” would be a better translation, but “Diet” is official.

³ The LDP is at the center of policy-making, and has developed an elaborate organizational structure within the party paralleling the organs of the Diet and the Ministries. But the factions are not unified actors in policy-making. There is some evidence of policy agreement within the “extreme” factions—the Kishi-Fukuda and Nakasone factions, for instance—but it is clear that most factions contain serious internal divisions on policy, and that the factions do not usually attempt to set a policy “line” for their members. All this does not deny, of course, that faction leaders may play an important part in policy making.

⁴ But for a different view, see for example, Scalapino, R. and Masumi, J., Parties and Politics in Contemporary Japan (Berkeley: Univ. of Calif. Press, 1962), passim Google Scholar.

⁵ On earlier methods of choosing Japanese political party leaders, see Tsuneo, Watanabe, Toshu to Seito (Party and Party Leader), (Tokyo: Kobundo, 1961), Chap. 7Google Scholar, and the same author's Seiji no Misshitsu (The “Smoke-filled Room” of Politics) (Tokyo: Sekkasha, 1966)Google Scholar.

⁶ The terms are those used by Japanese news-paper reporters. The present and following historical remarks in the text are based on the vernacular press of the time.

⁷ This does not touch at all upon the fascinating question of what maintains the factions. See Totten, G. O. and Kawakami, T., “The Functions of Factionalism in Japanese Politics,” Pacific Affairs (1966); 109–122 Google Scholar; Tsuneo, Watanabe, Habatsu: Nihon Hoshuto no Bunseki (Factions: An Analysis of Japan's Conservative Party), (Tokyo: Kobundo, rev. ed., 1964), Chap. 10Google Scholar; and Tamio, Kawakami, “Habatsu Rikigaku ni tsuite no Ichi Kosatsu” (A Study of the Dynamics of Factions”), in Kodo Kagaku Kenkyu (Behavioral Science Research) 2 (1966), 29–36 Google Scholar.

⁸ The most informative and perceptive research on the LDP factions in English has been done by Hans H. Baerwald. See his “Factional Politics in Japan,” Current History 46 (04, 1964), 223–229 Google Scholar, and his yearly summaries of developments in the January issue of Asian Survey, 1964, 1965, 1967. The best description of the history of LDP presidential elections is in Watanabe, Habatsu, op. cit., Chap. 9.

⁹ Mr. Ishii is presently Speaker of the Lower House. Mr. Ono held various posts in his long career, including the LDP vice presidency under Prime Ministers Kishi and Ikeda, but died in 1964. Miki Takeo is presently Foreign Minister. Mr. Kono was a perennial strong-man in many Cabinets, and a leading contender for the Prime Ministership, until his death in 1965. Fukuda Takeo later served as Minister of Finance, and is presently the Secretary-General of the LDP. Kawashima Shojiro is a pre-war party veteran who has held various Cabinet and party posts; currently he is the LDP vice president. His faction emerged from the Kishi faction when the latter split in 1961. Fujiyama Aiichiro, for many years president of the Japan Chamber of Commerce, entered full-time politics to become Prime Minister Kishi's Foreign Minister in 1957. His faction was also built up largely out of the old Kishi faction. He was the opposition candidate versus Mr. Sato in Dec., 1966.

¹⁰ Prime Ministers Kishi, Ikeda, and Sato won in uncontested elections in 1957, 1962, and 1964, respectively.

¹¹ The question of why Prime Minister Ikeda changed his coalition is answered, in a narrow sense at least, by the observation that the break-up of the old Kishi faction created a new situation.

¹² The N-M volume is now available in a Science Editions paper back(1964). The following relies on the formulation of Shapley, L. S. and Shubik, M., “Solutions of n-person Games with Ordinal Utilities,” Econometrica 21 (1953), 348–349 Google Scholar, with one important modification (avoiding the notion of an “effective set”) which was suggested by Aumann, R. J. and Peleg, B., “Von Neumann-Morgenstern Solutions to Cooperative Games without Side-Payments,” Bull. Amer. Math. Soc. 66 (1960), 173ffCrossRefGoogle Scholar.

¹³ This is the N-M definition. Shapley has refined the concept: according to his classification the definition in the text is of a “strong simple game.” See Shapley, L. S., “Simple Games,” Behav. Sci. 7 (01, 1962), 59–66 CrossRefGoogle Scholar.

¹⁴ Until this point, interval scale measurement has not been assumed, but strictly speaking this statement is meaningless without such an assumption. However, in a situation where the actual physical quantities which underlie the payoffs are in fact constant (as when there are simply 17 Cabinet posts, for example), then I feel that it may be permissible to speak of “constant-sum” without actually demonstrating that interval scale measurement is possible. (And, of course, one can certainly speak of constant-sum without implying that utility is linear with money or some medium of exchange; i.e., there is no assumption here that utility is “transferable.”)

¹⁵ This was proven by N-M, but the idea is intuitively clear also. If there is a W ^m and an actor j not in the W ^m, then by the constant-sum condition, v(W ^m) = v(W ^m + j). So j is unnecessary, from W ^m's viewpoint. Any payoff which the members of W ^m can get, they can get without j's help. Thus only W ^m needs to be considered when calculating dominance relations among payoff vectors.

¹⁶ Actually the problem of assigning weights is more complex than this hurried treatment shows. Two key questions are: do the weights make blocking coalitions impossible, and is the sum of the weights in any W ^m always the same? The N-M theory, as they formulated it and as used here, only applies if both of these questions can be answered positively.

¹⁷ See the Sources to Table 2 for an explanation of the meaning and the use made here of “intangible” factors. Briefly, the intangible factors I considered in assigning the factions' weights were (1) the financial backing of each faction, and (2) the likelihood that the “others” (not-factionally-aligned LDP members) would support each faction. These factors had to be considered, in assigning weights, since the percentages based upon memberships do not have the properties which N-M theory requires for weights. (See footnote 16.)

However, in the analyses of Sections III, IV, and V, I have used only the memberships of the factions, and a definition of “majority” as 51% of LDP Dietmen, when dealing with coalitions. The weights given in Table 2 were used only for making predictions on payoffs, as in Table 4. (Using the weights would not change any results for N-M theory, but using memberships makes it possible to contrast N-M theory with Riker's and Gamson's theories, as in Section IV.)

¹⁸ This is not how N-M put it; see Section 50.8.1 in N-M. The reason for this phrasing is given in footnote 22.

¹⁹ The reader can verify by inspection that none of these vectors dominates another. That one of these vectors dominates any other which is not in the solution will become clear simply by imagining some other vector and comparing it with these. For example, take (0, 1/3, 1/4, 1/4, 1/4, 0), for Kishi-Sato, Ikeda, Kono, Ono, Miki, and Ishii, respectively. Incidentally, it is known that N-M solution payoffs in situations like the present have a very desirable property: any deviation from a payoff vector in the solution set guarantees that the actor who benefited from the deviation will be absolutely worse off when a solution vector is re-imposed (as “must” happen, since the solution vectors dominate all others). See Vickrey, W., “Self-Policing Properties of Certain Imputation Sets,” in Tucker, A. W. and Luce, R. D. (eds.), Contributions to the Theory of Games IV (Princeton: Princeton Univ. Press, 1959), pp. 213ffGoogle Scholar.

²⁰ In honesty, it must be admitted that these two propositions contradict an essential feature of the N-M concept of a solution, namely, that it is possible for any outcome in the solution set to occur. This contradiction points to a serious weakness in my theory. (Cf. footnote 25.)

²¹ In the following section a model of coalition maintenance is described, and a proposition (by which maintenance is “easily explained” in the sense used above) concerning inter-decision period payoffs is derived from the model. However, that model was discovered ad hoc (which is the reason why it is discussed in the following section).

²² Thus, even if the N-M solution is not known, and even if payoffs are not measured on an interval scale, this proposition—derived from N-M theory as a logical consequence—can be applied!

²³ This definition of a winning coalition clarifies the meaning of the assumption that the prefectural delegates do not affect the party presidential election. That is, a winning coalition must be able to win in the LDP Diet factions' struggle, without the aid of the prefectural delegates. While the former wording may seem unjustified, the latter certainly reflects the real situation, in my opinion.

²⁴ Figures on factions' memberships have been drawn from the vernacular press, plus the books of Watanabe cited in footnotes 5 and 7, the Asahi Nenkan, the Kokkai Binran, the Asahi Journal (weekly), and the Gendai no Me (monthly). The newspapers contain about 40 independent estimates of the strength of each faction in the Lower House at 12 different times since 1955, usually just before and after a general election or LDP presidential election, and the other sources contain about another 10 estimates. (A dotted line indicates a general election.) Of the total of roughly 50 independent estimates, 22 list the names of all the members of each faction as well. Thus I obtained 12 reliable estimates of the strength of each Lower House faction, by taking the average of the 3, 4, or 5 estimates available for each point in time. The same sources and procedure were used for the Upper House. However, since until 1963–64 most of the LDP Upper House members were not tied to a particular faction but rather to one of three clubs, it was necessary to estimate the proportion of a club which belonged to one of the factions in that club. (This was done on the basis of reported voting in Upper House elections, such as for LDP caucus chairman, and in the LDP presidential elections.) But the Kishi and Sato factions in the Upper House have always made up one club by themselves; those figures are precise, based on the names in the official membership list.

Insofar as the “weights” differ from the memberships, this is due to information on the financial strengths of the factions, and on the ties between various of the “others” and the factions. Data on finances was obtained from the Kampo, the Official Report (of the Government), all months since 1956. This data was not used precisely, because reporters, politicians, and factions' staffers assured me that the data is not reliable; instead, relying on my data, which agrees with the widespread rumor that Kishi, Sato, and Ikeda (and Ishii, slightly) have the strongest financial backing, I gave these factions a slight edge when memberships were not clearly decisive. Similarly, depending on newspaper reports of the ties and attitudes of the “independents,” I gave the appropriate factions a slight advantage in figuring the proper weights.

For example, in January, 1959, the Kampo data show that the factions with the strongest financial backing (in 1958) were Kishi-Sato, Ikeda, and Ishii, while contemporary newspapers said that the small Ishibashi faction was thoroughly hostile to Kishi, although unable to agree upon a leader among themselves to succeed the ailing Ishibashi. Moreover, the neutrals were said to include a group who were close to or indebted to Prime Minister Kishi, although unable to admit this publicly by joining his faction. Finally, the rest of the neutrals included a group of ex-Liberal Party members who were said to be willing to support either Kishi-Sato or Ikeda, whichever was more expedient, but did not want them to fight each other. On the basis of this information, I reasoned as follows.

a. Kishi + Ikeda are already winning (51%), and in reality they are even stronger than their memberships indicate;

b. Kishi + any two of Kono, Ono, Miki, and Ishii are already winning (54% or 56%), and in reality may be slightly stronger than their memberships indicate;

c. neither Ikeda+any three of Kono, Ono, Miki, and Ishii, nor Kishi + any one of the same four, is winning on the basis of the memberships; considering the Ishibashi faction's hostility to Kishi, its 4% can always be counted in with the anti-Kishi coalition; financially, an Ikeda vs. Kishi fight would rather evenly split the big money; the neutrals would also divide rather evenly. Hence these calculations seem reasonable:

Ikeda + Kono + Ono + Miki

=44 + Ishibashi's4 + 3½ neutrals = 51½

Ikeda + Kono + Ono + Ishii = ditto

Ikeda + Ono + Miki + Ishii = ditto

Ikeda + Kono + Miki + Ishii

= 42 + Ishibashi's 4 + 3½ neutrals = 49½

But still, this last coalition too would be winning if it should form, even versus Kishi-Sato + Ono + 3½ neutrals = 50½, since Ikeda and Ishii—with their money and their influence in the ex-Liberal Party-dominated Ono faction—could break the unity of the Ono faction (especially in the Upper House, where Ono's extra strength lay).

In short, in this typical example of the calculations behind Table 2's weights, the memberships determined which were the W ^m for seven coalitions, the memberships plus the factors of money and unofficial ties determined three other minimal winning coalitions, and those factors plus an arbitrary judgment based upon knowledge of probable defections decided the last W ^m.

²⁵ The assumption that the posts are or reflect all the winnings to be won seems valid except for one serious problem. It is not correct to say that a faction leader's calculations regarding his future chances of succeding to the Prime Ministership depend solely upon the posts his faction wins. Moreover, such calculations about future potentialities seem to be very important in determining the strategies and tactics chosen by faction leaders. The failure to include in the operational definition of payoff anything corresponding to these calculations about the future is a second serious weakness in my research. (Cf. footnote 20.)

²⁶ Of course, any list such as this can be criticized. There is not space here to raise and answer all of the possible questions which should be asked Three omissions must be explained, however. The Chief Cabinet Secretary (kanbochokan) I have lumped together with the Prime Ministership, since the former is always a “right-hand man” of the P. M. The political under-secretaries (seimujikan) I have omitted on the advice of several newspapermen who insisted that these posts are not part of the same “game.” Diet posts—committee chairmanships, speakerships, etc.—are omitted for the same cause: they are given to individuals, and for reasons which are different from the reasons governing the distribution of Cabinet and top party posts.

²⁷ Thus, while the measurement of the payoffs is only ordinal scale level, because the physical “goods” which underlie the payoffs are a constant amount for any winning coalition, and because all the factions do in fact want these posts roughly equally badly, it seems defensible to claim that the situation is constant-sum. (See footnote 14, above.)

²⁸ Many observers would dispute this interpretation, arguing that Ikeda himself actually double-crossed Kono, under the influence of one of his close aids, Ohira Masayoshi, who was very friendly with Mr. Sato's top advisor, Tanaka Kakuei. See, e.g., Baerwald, Hans, “Japan: The Politics of Transition,” Asian Survey 5 (01, 1965), especially pp. 34–38 CrossRefGoogle Scholar. Others would simply assert that it was fore-ordained that Sato follow Ikeda, by ex-Prime Ministers Yoshida and Kishi and the business community. Both of these explanations would have Mr. Miki merely realizing which way the wind was blowing, and trimming his sails to fit it. But I have talked with some political insiders who feel that Mr. Miki's switch to support of Mr. Sato came first, and was the main cause of Prime Minister Ikeda's decision to nominate Mr. Sato.

²⁹ At this time, just after the formation of the LDP, there were three major streams within the party: former Liberals, former Progressives, and people who bolted from the Liberal Party during 1953–54. Tabulating each faction's members' ties with these three streams shows marked differences. (Using data in the Seito-kai-ha Hen of the Gikai Seido 70 Nenshi.) An analysis of the composition of the three factional alliances which existed in 12/66, in terms of these ties, assuming that an alliance is more likely to join with another alliance if their members share the same historical ties, leads to the conclusion that, of the two possible 5-member winning coalitions, the Ishii-Ikeda-Ono-Miki-Ishibashi coalition was much more likely to form!

³⁰ Ambiguity occurs because the payoffs are only ranked; distances between two ranks are unknown. E.g., it is not clear whether a payoff of 2c + 2e is greater or less than a payoff of 3d + f. The ambiguous cases are identified below. Two cases which are strictly speaking ambiguous I have classified as clear because they seem unquestionable: K-S vs. Ikeda in 7/60, and Ikeda vs. Ono in 7/63. (I.e., I assert that 5c>b + d + e; and that b>c + f.) Of course, to call these two cases ambiguous would not make N-M's correct predictions on them into failures; it would just remove them from the analysis.

³¹ See Riker, W., The Theory of Political Coalitions (New Haven: Yale Univ. Press, 1962)Google Scholar, and Gamson, W. A., “A Theory of Coalition Formation,” Amer. Sociol. Rev. 26 (06, 1961), 373–382 CrossRefGoogle Scholar. The Shapley theory of value, which John C. Harsanyi and others have developed further, is best known to political scientists in the guise of the Shapley-Shubik a priori power index; see L. S. Shapley and M. Shubik, “A Method for Evaluating the Distribution of Power in a Committee System,” this Review, 48 (1954), 787–792. What I call the newspapers' theory is one of several common sense explanations of “the game of politics in Japan.” Two others are mentioned in the parenthesis.

³² The “traditionalistic factors proposition” is not disconfirmable because there are so many such factors; after the fact it is always possible to find some such explanation. The “zaikai proposition” is not disconfirmable because the zaikai is not, usually, unified; some part of the zaikai “wins,” even when an Ishibashi defeats a Kishi. Of course, to be not disconfirmable is not to be incorrect, just useless for present purposes.

³³ Gamson explicitly states that his theory's predictions depend on resources. Riker says “weights,” but in his own applications uses memberships. (If Riker's weights are the same as N-M's weights, then his theory is no different from theirs.)

³⁴ This manuscript was completed in June, 1967. In December, 1967, Prime Minister Sato reshuffled his Cabinet and changed most of the top LDP executives. Messrs. Nakasone, Kawashima, Miki, Ishii, and Fukuda are now all in some top position in the Government or party, as is the number two leader of the former Ikeda faction (Ohira Masayoshi). The total distribution of rewards is as follows (with the December, 1966, payoffs from Table 3 included for comparison). The single post (an “e”) given to the satellites of the Sato faction is included in the rewards for the latter. Also, incidentally, the allotment of Parliamentary Vice Ministerships (seimujikan) did not follow the same pattern as this distribution of major rewards. Rather, the Maeo and Nakasone factions received three and four, respectively, while the Sato and Kishi-Fukuda factions received five and two, respectively. The Miki and Ishii factions received one each, and the Fujiyama, Funada, and Kawashima factions received none.

This change in the distribution of rewards from 12/66 to 11/67 is an excellent example of the maintenance proposition at work. Prime Minister Sato is attempting to hold together his old support coalition (asterisked factions), while making overtures toward the major opposition factions, Maeo and Nakasone. The effect of Mr. Sato's skillful reshuffle is to have made it possible for the Maeo and Nakasone factions to consider supporting Mr. Sato in the coming LDP presidential election this fall. Therefore the conclusion above, that the Miki faction will determine the outcome of the forthcoming election by choosing between Kishi-Sato + Miki and Maeo + Nakasone + Miki + Kawashima, is no longer valid. Rather, the Kishi-Sato bloc would appear to have the option of coalescing with a variety of partners in different winning coalitions.