were generally strongest in the large industrial states with the support of big city and ethnic voters who allegedly exercise disproportional influence in presidential elections. Except for the somewhat disproportional southern support for the Democratic ticket in 1960, the Democratic coalitions can be termed the more liberal of the major party coalitions. In 1968 the Democratic coalition was shorn of its disproportional southern support and thus was even more dependent on the big city northern groups that the conventional wisdom asserts are especially effective in presidential elections.

If these groups cast disproportional weight, it should have produced a Democratic advantage in 1968, but our measures of the swing bias, which indicated a modest Democratic advantage in 1960, shifted to a stronger disadvantage in 1968. Strangely, by the standard interpretation, Humphrey apparently improved on Kennedy's support generally in the large industrial states despite running behind in the relative popular vote contest nationally. Kennedy won only 51.1 percent of the two-party votes in the nine biggest states which contained a majority of the nation's population in 1960, while Humphrey won 51.4 percent of the two-party votes in these same states." Nevertheless, Kennedy won seven of these nine states for 180 electoral votes compared to only five states with 128 votes for Humphrey because Kennedy's popular strength was better distributed within the large states, a phenomenon that is unrecognized by the conventional wisdom about distributional biases. An examination of Table 6 suggests some of the problems with Humphrey's distribution in the big states. Although nationally somewhat less popular than Kennedy relative to Nixon, Humphrey picked up relative popular support in five of the nine states and lost support in four. The largest changes in relative Democratic support between 1960 and 1968 brought increased Democratic suport in Massachusetts and Michigan, where additional support was not needed. Humphrey ran slightly behind Kennedy in Illinois and New Jersey, which cost him those two states. Since better distribution within these nine states alone would have blocked the election of Richard Nixon, Hnumphrey's over-concentration of support in some of the largest states facilitated the election of Nixon.

Table 6 clearly indicates that Kennedy's election in 1960 depended in large part on his ability to carry large blocs of electoral votes by very slim margins compared to Nixon's generally more substantial margins. Part of this is accounted for by the highly competitive voting in the large states when the national voting is highly competitive. Paper thin majorities are efficient in carrying electoral votes with minimum popular support but they are also vulnerable to upset with very slight changes in the behavior of the electorate.

TABLE 6.-IDENTIFICATION OF PIVOTAL STATES IN 1960 AND 1968 WITH STATES SUPPORTING MAJOR PARTIES RANKED BY DEMOCRATIC PERCENTAGE OF 2-PARTY VOTES

32 The nine largest states with the largest blocs of electoral votes in 1960 were New York. California, Pennsylvania, Illinois, Ohio. Texas. Michigan, New Jersey, and Massachusetts. After the 1960 census Florida was apportioned the same votes as Massachusetts which had previously been the ninth largest state. The nine largest states in the 1960 election were selected for comparison because they contained a majority of the nation's population and except for Texas were the northern states deemed particularly decisive by the conventional wisdom.

TABLE 6.-IDENTIFICATION OF PIVOTAL STATES IN 1960 AND 1968 WITH STATES SUPPORTING MAJOR PARTIES RANKED BY DEMOCRATIC PERCENTAGE OF 2-PARTY VOTES-Continued

TABLE 6.—IDENTIFICATION OF PIVOTAL STATES IN 1960 AND 1968 WITH STATES SUPPORTING MAJOR PARTIES RANKED BY DEMOCRATIC PERCENTAGE OF 2-PARTY VOTES-Continued

1 The State of Mississippi firmly withheld its 8 electoral votes from either major coalition. 29 States with the largest blocs of electoral votes in the 1960 election and containing a majority of the Nation's population. 36 members of the Democratic ticket in Alabama were not loyal to the national ticket; however, the same States remain pivotal without those votes under the actual apportionment.

5 States firmly withheld their combined 45 electoral votes from either major coalition. They were Alabama, Arkansas Georgia, Louisiana, and Mississippi.

With the Democratic coalitions of 1960 and 1968 remarkably similar to the ordering of the state pluralities except in the South, it appears that Humphrey was the victim of the modern pattern of biases in which major parties are competitive throughout the nation, and small alterations in the distribution of coalitions can work both for and against the same basic type of voter coalition in unpredictable ways. That Humphrey was hurt mainly by the asymmetry of the state pluralities is confirmed by considering the measures based on projecting minimum winning coalitions as reported in Table 5. Comparison of Table 5 parts A and B indicates that the constant two bias alone in 1968 was insufficient to produce any net bias measured to a tenth of a percentage point. The malapportionment bias measured in Table 5C was only slightly against the Humphrey voting coalition and must be sharply discounted because of the competitiveness of the two major coalitions throughout the states. This leaves the asymmetry of state pluralities to account for the substantial net bias against the 1968 Humphrey coalition.

METHODOLOGY AND THE STUDY OF POLITICS

The key methodological errors of the conventional wisdom and its symbolic relationship with game theoretical models derived from probability theory can now be summed up. First, the conventional wisdom rested on a failure to conduct a comprehensive analysis of the complex of biases affecting the interaction of the electoral rules with voter distribution relevant to policy preferences. The complex of biases involving the constant two votes, residual malapportionment, bloc voting by states, voter turnout, and the size and symmetry of state pluralities led scholars to focus on some segments of the system of biases to the exclusion of other interacting biases. Proponents of the conventional wisdom have also been overawed by the pivotal states and decisive pluralities without considering the core coalitions that determine what states and voters have a chance to claim to swing elections between coalitions. They thus tend to load all the policy consequences on the votes of the citizens of the pivotal states where the major coalitions are most competitive.

33

This appears in the argument for retaining the electoral college by such spokesmen for the conventional wisdom as Wallace Sayre and Judith Parris. They are so impressed by the small pluralities they see swaying decisively large blocs of electoral votes under the present system that they predict that direct election would dramatically shift the attention of presidential contenders toward the less competitive states with important policy consequences. Attributing their conclusions to a "non-exact science", Sayre and Parris apply no rigorous test of their thesis, and thus overlook the impact that the shift of a coalition's policy appeal to the less politically competitive states might have on the voters in states that are now highly competitive.

33 Sayre and Parris, op. cit., pp. 71-72.

The probabilistic models of electoral power of voters support the conventional wisdom by supplying apparently rigorous analysis to the essentially impressionistic arguments of the more traditional scholars supporting the liberal bias thesis. Although seemingly worlds apart methodologically, both the traditional and the game theoretic approaches share the same fundamental methodological weakness. They both focus on marginal "decisive" voters to the exclusion of the underlying interstate coalitions. While appearing to introduce mathematical rigor, the probabilistic models exclude more relevant political information than their proponents seem to realize. This flaw in the probabilistic models has not received adequate challenge, I suspect, because the indices generated seem to confirm the conventional wisdom. The symbiotic relationship of the conventional wisdom and the probabilistic models appears in recent articles in the APSR. Stephen Brams and Morton Davis, for instance, present a model of electoral college biases measuring the probabilities of "uncommitted voters" swaying to particular tickets once the basic appeals of the tickets have been established."

Excluding considerations of policy-based coalitions and indeed all appeals cutting across state lines allows the assumption that the probability of uncommitted voters in each state supporting a ticket is determined by the relative apportionment among the states of campaign resources, such as the candidates' time. Adding the assumptions that committed votes are evenly split between the tickets in each state and that the uncommitted are distributed proportionally across the states, Brams and Davis conclude that electoral support is maximized by devoting disproportional campaign resources to the more populous states. Because the precise optimal allocation for a ticket depends on the allocation of the opposition, it is highly unstable. But, they argue, the best strategy for presidential tickets with equal campaign resources divisible among the states is to allot these resources to states in the ratio of their populations raised to the 3/2 power. Their finding that the attractiveness of voters increases with state size should not surprise us because it rests on the same Central Limit Theorem of probability distributions that generates Benzhaf's power index of 3.312 for the relative power of the largest state's citizen voters based on the 1960 census apportionment. Brams and Davis report a comparable index of 2.92 for the relative attractiveness of voters in the largest state as campaign targets based on the 1970 census apportionment.

The analysis of decisive uncommitted voters presented by Brams and Davis is equally misleading in its apparent confirmation of the conventional wisdom be cause their model excludes consideration of policy-oriented coalitions by assuming that the committed voters are equally divided between the tickets in each state. All that remains to influence campaign appeals is voters so uncommitted that given equal allocations of campaign time by the preseidential tickets in each state, they are equally likely to support either ticket. Worse yet, Brams and Davis fail to recognize the limitations of their model for analyzing the policy consequences of the electoral system. They misakenly conclude that the attractiveness of large state "urban" voters gives "disproportional weight to the attitudes and opinions of the voters of these states". The influence of the conventional wisdom is so great that no one has noted that voters with any special attitudes or opinions would tend to commit themselves to particular coalitions and thus fall outside the terms of the Brams and Davis model, which treats only "uncommitted voters." Attention to the model's limiting assumptions reveals that it can not measure the impact of the electoral rules on policy-oriented coalitions. As demonstrated in examination of the limitations of the Banzhaf model. information about voting behavior is incompatible with models based on the random formation of coalitions, and tying the probabilities to campaign allocations still leaves voter choice essentially a random phenomenon, Brams and Davis may present an internally valid mathematical model by confining their calculations to the "uncommitted voter" concept, but they underestimate how that limits the model's external validity. They believe the external validity of their model is confirmed because acual allocation of campaign time is somewhat better predicted by the 3/2 power rule than by a simple proportional distribution. Ordeshook and collegaues rightly argue in rebuttal that there are other reasons for expecting disproportional campaign allocations to the large states. The core

4 Stephen J. Brams and Morton D. Davis. "The 3/2's Rule of Presidential Campaigning." American Political Science Review, v. 68 (March 1974), pp. 113-134; and Brams and Davis Comment on 'Campaign Resource. Allocation Under the Electoral College'," American Political Science Review, v. 69 (March 1975), pp. 155-156.

35 Brams and Davis. "The 3/2's Rule of Presidential Campaigning," Ibid., p. 134. 30 Claude S. Colantoni, Terrence J. Levesque, and Peter C. Ordeshook, "Campaign Resource Allocations Under The Electoral College" (with Comment by Brams and Davis and Rejoinder), American Political Science Review, v. 69 (March 1975), pp. 141-161.

coalition model, which unlike the probabilistic models incorporates information about the relative competitiveness of policy-oriented coalitions, also disproportionately identifies the more populous states as pivotal. The correlation of political competition and constituency size has been noted by students of American politics from Madison to McConnell, information which is excluded from the game theoretical models that we have examined."

Campaign managers with resources capable of attracting additional voter support in individual states independent of the general appeal of coalitions will indeed want to concentrate sparse resources in competitive states with large blocs of electoral votes, but campaign budgets are not central to policy choice. It is the underlying coalitions themselves that determine which states are so competitive that the outcome might rest on such influences as motorcade itinerary. Moreover, the analysis of policy-oriented coalitions suggests that the distributional biases tend to be small and therefore the overall voter appeal of a party ticket must take precedence over attempts to seek distributional advantages. Focusing on while coalitions also avoids loading policy consequences on so-called "swing" voters in the pivotal states where the underlying coalitions are most competitive and decisive voters can be basically indifferent about policy. Not only do traditional proponents of the conventional wisdom tend to focus on "swing" voters to the exclusion of the coalitions that make certain states critical, but the probabilistic models have this focus by definition. They treat coalitions as essentially randomly organized so that they may compute the probabilities of some voters swaying an election between rival coalitions. This denigration of the relevance of the distribution of rival coalitions themselves is also reflected in the most recent version of the probabilistic model appearing in the APSR. Although Guillermo Owen states that his mode is "quite different" from that of Brams and Davis, his model also assumes the random formation of coalitions and confines the analysis to the impact of state population sizes on the probabilities of certain voters "deciding" the electoral vote winner. Because the model rests on relative probabilities, the Central Limit Theorem is also fundamental to his computations of the state size bias, and so it is not surprising that his power measures are also comparable to those of Brams and Davis. The variations of the probabilistic model appear to fit the conventional wisdom explains their wide circulation with sparse challenge to the applicability of the model's assumptions to political analysis.

It may also help that the sophisticated mathematics employed with variations of the probabilistic model are beyond the capacity of most political scientists. The alternative analysis that I have presented is not only well within the methodological capabilities of political scientists willing to reexamine the propositions of the conventional wisdom, but it is suitable for analyzing the interaction of the electoral rules with policy-oriented coalitions. This politics-oriented analysis mounts a serious challenge to both the conventional wisdom and the false inferences drawn from game theory models based on probability theory. Whatever the merits of avoiding a truly national election of the President, the thesis that the electoral college has served the special policy interests of liberals, ethnics, and city residents is disconfirmed by my analysis. Not only do the measured biases conflict with the conventional wisdom, but they only worked in a consistent direction when constitutional rights of free political competition were violated. Granted national voter rights, the residual biases are too sensitive to slight shifts in voting coalitions to reliably favor particular policy-oriented coalitions.

In identifying the methodological flaws in the support for the conventional wisdom, my analysis suggests the need for caution in drawing inferences from mathematical models. This is not to argue against introducing mathematical rigor into our political analysis because if we properly understand the assumptions inherent in a particular model, we will find warnings about inferences that are not warranted by the model. Such warnings were identified in the probabilistic models, but other scholars ignored them because the models were mathematically sophisticated and seemed to confirm the conventional wisdom. The probabilistic models appealed to both the methodologically unsophisticated students of politics already impressed by the conventional wisdom and the game theorists who virtually treat political science as a subdiscipline of mathematics. As social scientists we must seek methodological procedures useful to our explorations of politics, but in borrowing sophisticated mathematical tools we must be wary 37 James Madison, Federalist Papers, #10; and Grant McConnell, Private Power and American Democracy (New York: Knopf, 1967).

Guillermo Owen, "Evaluation of a Presidential Game," American Political Science Review, v. 69 (September 1975), pp. 947–953.