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shared those votes the result would be the same. Thus, 100 miror candidates could cause an electoral deadlock without carrying a single state. More strikingly. a major candidate could earry every state, something that requires such overwhelming support that no candidate has ever done it, and still not win the presidency under raw voting.

To make a realistic comparison of relative risks, let us assume that, under raw voting, the popular vote divided as (40, 35, 35) percent, which is at deadlock and allows, roughly, as substantial a third-party vote as is consistent with a distine tion between major and minor parties. We have chosen these numbers so that the difference between the two major candidates is half the difference between the third-party, and the lesser major, candidate. At this point, there is very serious danger of a deadlock under raw voting, and it corresponds to about a 17.5 million popular vote for the low man. That vote, under natural roting, would produce a deadlock only if 16 million of those votes had been polled in states carried by the candidate. That is, while the candidate polled 25 percent of the votes, he must have distributed them so that about 91 percent lay in states he carried. This might argue very broad support. Eisenhower placed roughly that fraction of his votes, in 1952, in states that he carried, but he was a landslide winner, not a third-party splinter candidate. The man might also be a strong regional candidate, but unless he concentrated his support in a very few states (they would have to be very large ones) he would win a great many electoral votes, and no longer merit the name "splinter" candidate. In short, a candidate who wins 16 million votes in the states he carries, is very likely to have polled 30 or 40 million votes in all, particularly in a three-candidate election. It is unlikely then, that any candidate would count on causing a deadlock, since the support required would give him an excellent chance at victory.

For elections in which four or more candidates attract large support, the natural method performs, if that is possible, even more satisfactorily. Deadlock becomes less likely because the fraction of votes earned by the candidate who carries a state is likely to be smaller in such an election than in one with fewer candidates. Thus, when his votes are removed, fewer of them must be subtracted from the total number of electoral votes cast, and the election is less likely to fail. On the other hand, candidates that are eliminated later in the states he carried, do not threaten the system since the votes cast for them go to the highest candidate in that state, and are not eliminated. In short, only votes cast for splinter candidates in the states they have carried can threaten deadlock. As the number of splinter candidates increases, that critical number decreases, as does the risk. By contrast, the other two methods become increasingly dangerous with the addition of successive, serious candidates.

Finally, we might mention that raw, proportional, and natural voting can be characterized by a single number n. If electoral votes are divided among candidates according to the nth powers, v", of their respective votes, then n=1 gives raw and proportional, and n=0, natural (i.e. winner-take-all) voting, in any state.

This emphasizes that the various proposed systems are really similar, of the same class, and can be analyzed together. Assume for example, that two candidates polled 5 and 3 votes, respectively, in a hypothetical "state". Under a system in which n=1, their respective shares of the state's electoral votes would be proportional to 5-=5, and 3=3. The first candidate would receive 58, the second, 30, of the states votes. This is the condition of raw or proportional voting. Under an n=2 system, the first candidate would capture a share proportional to 59=25. as against 3=9 for his opponent. Thus, the votes would divide (55, 3) for n=1; (25/34, 934) for n=2; (125/152, 27152) for n=3; and (1, 0) for n=o. Expressed as percent of total electoral vote received, these numbers are (62.5, 73.5, 82.2, ..., 100.0) for the shares of the larger candidate with values of n=1, 2, 3, ...00.

From the point-of-view of any state then, the ideal value of n will depend on whether the state is balanced or unbalanced. A balanced state will want a high n (such as in winner-take-all voting) so that a small advantage in the state will be worth contesting and negotiating for. Unbalanced states, on the other hand, will want a small n, since a large n reduces the advantage of vigorous campaigning. Such a state would like to be rewarded for loyalty and enthusiasm in its voters, but if the advantage of a one-vote plurality is the same as that of a millionvote plurality, candidates are likely to be insensitive to such claims.

The simplest arrangement would permit states to decide their own values of n (that is, between raw voting, winner-take-all and all the systems between). This system fails if the decision is made by popular vote in unbalanced states. There party advantage defeats state advantage and the voters of the leading party, rather than concede a portion of their state's eleotoral vote to the opposition, are likely to insist on a winner-take-all system. This predicts that if the states were given their choice, all would select the winner-take-all method : the balanced states, because it enhances the value of votes cast, the unbalanced states, because it enhances the power of the leading party. In the only similar actual case, this tendency is actually observed. At present, all states, balanced or unbalanced, have chosen winner-take-all methods of apportioning their electoral votes.

The point that emerges is that the ideal choice of system from the Jeffersonian point-of-view, is dictated by the balance of the state, but there is no way, short of a radical Constitutional change of state powers, to enforce the Jeffersonian ideal on an unbalanced state. The effect of natural voting, however, is to achieve much of this goal by placing with the individual the option of voting "No Candidate". In unbalanced states containing disaffected individual voters, winner-takeall voting becomes, in effect, equivalent to proportional or raw voting, for majority voters. Suppose 7 million voters of a state vote for the majority, and 3 million opposition voters cast "No Candidate" ballots. Under natural voting, the majority candidate gets the same number of electoral votes as he would have had under proportional voting. The minority candidate, of course, doesn't receive the votes of his supporters. Thus, fully half of the advantage of proportional voting is secured by unbalanced states every majority vote is valuable to the winning candidate, and the minority votes do not count for the winner. Moreover, the balanced states maintain the system ideal for them, at the same time.

CONCLUSION The electoral system we have now is perhaps the most successful in all history, despite its shortcomings. In regulating the most dangerous political process we face, that system bas safely survived nearly two centuries of the most rapid national growth and acute strife without major amendment. More impressive perhaps is its success in moderating the tensions between various regions of one of the largest countries on earth, and between the largest and smallest of its states. There has not been, probably, so successful and powerful a republic, ruled by democratic principles, at least for the last two thousand years. By contrast the major reforms propose systems that have never succeeded or endured.

Simple popular election has been the means of destruction of too many western republics for us to assume it is safe, and the technical analysis of individual voting power supports these suspicions even as the names of Hitler, Napoleon, Napoleon III realize them historically.

Our system is based, historically, not on majority-rule alone, but also on the principle of individual control of the institutions of government. This Jeffersonian principle is destroyed by, among others, the method of raw popular voting. Our present system provides this protection, and by making its base popular, nearly all its defects can be, we have argued, removed. From principles accepted by nearly all Americans, we have argued that the best simple system is the one we have called "natural" voting.

The maintenance of a strong individual voice in the choice of President makes the difference between a despotism (no matter how benevolent) and a responsive democracy. Since we cannot foresee the strains that future crises may impose, the only safe course is to ensure individual rights and liberties by providing individuals with a powerful voice in the selection of the President. With such a protection, brought about by the modest improvement of the successful method of the last 180-odd years, individuals can defend their other rights, and hold them despite the hostility of the majority, or the strains of crisis.

Perhaps the clearest statement of the need for vigilance in protecting the individual came from a man born in Jefferson's presidency, who wrote of his researches and observations of the political character of the presidency of Andrew Jackson, [9] "If ever the free institutions of America are destroyed, that event may be attributed to the omnipotence of the majority, which may, at some future time urge the minorities to desperation and oblige them to have recourse to physical force. Anarchy will be the result, but it will have been brought about by despotism."

APPENDIX

DERIVATION OF THE FORMULA Assume that among 2n uncommitted votes, candidate A needs 8 votes more than half (to overcome, for example, a lead of 28 won by, or conceded to, his opponent among the committed voters.) Assume further, that A's independent probability of winning any single uncommitted vote is p. We define the value of an uncommitted vote as the increase it would give to A's chances of winning by switching to him, if nothing else changed, times the value, N, of victory. Simply, the value of an individual vote to A is the increase in A's expectation that results from the switch of that vote to A.

With these assumptions, we can compute the value of a vote, or of a bloc of b votes, using the binominal distribution. Before the switch of the votes, A needed n + 8 votes of 2n; afterwards, n +8 – 0 votes of 2n . We can approximate the binomial distribution by the normal or Gaussian distribution to get a result that is useful near the average value. That is, it will give the right numerical answer, approximately, if A does not need too many more votes than he would expect by chance alone. In very severely unbalanced situations, the approximation fails, but we know the right answer without having to calculate. Small numbers of votes cannot make any appreciable difference in such situations, and their value must be nil.

Before the switch of b uncommitted votes to his cause, A could expect to poll I=2np. The spread, uncertainty, or standard deviation, o, in this estimate is o= (2np(1-p))1/2. The candidate needs at least nts votes, which is n +8-i votes more than his normal expectation, i, and H standard deviations above it, where

H=(n+8-1)/o. We may call H the relative handicap under which A operates before the switch of votes, and the probability of his overcoming it is given, according to the normal probability distribution, by

P(H)=(26)-1/2

-undu

(1)

After b votes are newly committed to him, A's relative handicap H is slightly lower, the integral in eq. (1) extends over a slightly larger region, and his probability of overcoming the new handicap will be greater. The increase is simply the integral of the normal distribution in the added region

AP(H)= (2+) % Se-vor du

which we can approximate by the width of the added region,

AH={(1-P)/o]-[6H/4n), multiplied by the height of the curve at the middle of the added region, P(H-(AH/2)). Even that approximation is unnecessarily detailed. We have assumed n large and H small, so that consistency suggests that we ignore the second term in brackets, containing H/n, in comparison with the first.

Let us call the leading term, in brackets above, I, where I=6(1-p)/o. It is the actual number of votes by which A's expectation increases when b uncommitted votes switch to him, measured, again, in units of o. Before the switch, A could have expected bp votes from among the bswitches, by chance alone; afterwards, b votes. Thus I is the vote increment carried by b votes, and H is the vote handicap under which A labors, both relative to the uncertainty, o, in A's final count. Using Eq. (2),

V(1,1)=(26)-1/2 NIe-(1-1/2)2/2

(3)

gives the value of an increment I, when A is under a handicap H, and where victory has the value N.

REFERENCES

1. Martin Shubik, ed. Game theory and related approaches to social behavior. New York: Wiley, 1964 in which see especially L. S. Shapley and Martin Shubik. “A method for evaluating the the distribution of power in a committee system.” Selection 9. Irwin Mann and L. S. Shapley. "The a priori voting strength of the electoral college." Selection 10.

2. Election of the President: Hearings before the Subcommittee on Constitutional Amendments of the Committee on the Judiciary, United States Senate, Eighty-ninth Congress, Second Session. Washington: U.S. Government Printing Office (Testimony of Paul A. Freund, Harvard Law School, and a member of the American Bar Association Commission on Electoral Reform) p. 368

3. New International Year Book, 1916. p. 745

4. (Testimony of Hon.' Roman L. Hruska, a U.S. Senator from the state of Nebraska. In [2] above, p. 24)

5. Testimony of John F. Banzhaf III, attorney at law, New York, New York. In (2) above p. 518, and p. 905)

6. Andrew Hacker. Congressional districting. Washington: The Brookings Institution, 1964. Revised Edition. a) Chapter 3, Political Cartography b) p. 42-43

7. Neal Peirce. The people's president. New York: Simon and Shuster, 1968.

8. (Testimony of the Hon. Birch E. Bayh, a U.S. Senator from the state of Indiana, chairman of the Subcommittee) In [2], p. 18.

9. Alexis de Tocqueville. Democracy in America. New York: Alfred Knopf, 1960. Vol. I, p. 269.

A CALIFORNIA PLAN To REFORM PRESIDENTIAL ELECTION PROCEDURES RETAINING

THE ELECTORAL COLLEGE AND GIVING MORE EFFECT TO THE NATIONWIDE POPULAR VOTE, BY WARREN PEARSON, INSTRUCTOR OF HISTORY, SANTA MARIA INTERNATIONAL ACADEMY

Moved to action by the agonizing extravaganza of uncertainty and apprehension of the night of November 5 just past, I write these lines to suggest a way out of such situations. I write to propound what I am calling "A California Plan" to reform the system of electing the President and Vice-President of the United States ... a plan so simple and so direct as to end, once and for all, any possibility of a constitutional crisis arising out of close elections for these office in the future. The Plan would require a constitutional amendment with four basic clauses :

(1) All existing provisions relating to the electoral college shall remain unchanged.

BUT (2) In all future elections for President, if no candidate shall receive a clear majority of otes in the electoral college as provided by existing law, then and then only the election shall be immediately decided by reference to the total number of votes cast by the Whole People of the United States, and the candidate receiving a plurality of such nationwide popular vote shall be declared duly elected to the office of President of the United States.

(3) The Vice-President shall be elected by an identical procedure

(4) All provisions of Amendment XII relating to the House of Representatives or otherwise inconsistent with the above shall be repealed. To determine the need for such a plan, and its merits, let us consider the election of 1968. It is news to no one that, in the late hours of Tuesday, November 5 and the morning hours of Wednesday, November 6, the whole nation faced the possibility, even at times the distinct probability, that there would be a stand-off in the vote of the electoral college, and that weeks of critical importance to the interests, or even the existence of the United States, might have to pass before Congress could meet and decide the issue of the election.

Consider also how narrowly this grave constitutional crisis was finally avoided. It failed to occur because of the vote of California ; but more than that, it failed to occur because of the vote in Orange, San Diego and Los Angeles Countie, in the order named, where large paralities decided the catcode for the entire state. Wiboat ruh an arra, seither of the two leading cocteodens wald have had a majority in the electoral college, bo winner could have been named by that body, and the constitutional crisis that all had feared to have me opon or wantry. They called the election a diff-hanger throne out that menerable evening, but wbo could have predicted that such a crisis world be avoided by the vote of just three counties in just one state?

And now for a supposition, or rather two suppositions. Suppose 11that ce the night of Tuesday, November 5, 1968, the constitutional ameadrest pro pwd try this Cabfornia Plan had been in full force and effects and that 121 all the mats had voted exactly as they did except California and these three cantins, and that California had gone to the other camp. In that eveat. xoak either candidate have received a clear majority in the electoral college? Xe, of (norme not, because a third candidate took 45 electoral votes and a clear majority was out of the question. Would there have been a constitutional crisis? Could there have been one? The answer is a ringing No to both questions de cause either Vice-President Humphrey or Richard M. Nixon was bound to outpoll the other and be declared duly elected to the office of President of the United States. Of the dread and apprehension that obsessed the minds of countless Americans as they watched the totals mount that evening there would not have been a trace.

Hurely this example demonstrates that this plan has advantage enough to merit the thoughtful consideration of the lawmakers of this country and of Its citizenry as a whole. It would retain the electoral college, and sbould therefore win the support of those millions who have rightfully insisted on the useful role it has played in the vast majority of the elections in the history of the United States. On the other hand it would give just and reasonable recognition of that principle espoused by other millions, that, in the last analysis the will of the people should prevail. The COMMINGLING of both these interents in one single Amendment lies at the very heart of the argument for its adoption, as we see in examining the reasons why so many prior attempts to re form election procedures have gone down to defeat.

But what of the House of Representatives in its role of arbiter of elections left unsettled by the electoral college? Does its record reveal anything resembling the promptness and fairness of decision, or conformity to the will of the people that is built right in to the Plan that is here heing urged ? Quite the reverse is true. Consider the election of 1824. In that elertion, which bore a striking re semblance to the election just past by reason of the presence of more than two contenders, the Democrat, Andrew Jackson had a plurality of 15 in the electoral college and a respectable plurality in the popular vote. Nevertheless, since he did not have a majority in the electoral college, the election went to the House, which unblushingly counted him out in favor of John Quincy Adams, who had been a double loser as we have just explained.

There is no indication whatever, nor any guarantee, that such a drama could not have been re-enacted in the event that EITHER Vice-President Humphrey or Mr. Nixon emerged the winner of the popular vote on that fateful Tuesday night. There is likewise no guarantee for the future against this sort of thing UNLESS THE SYSTEM IS CHANGED. In truth whatever assurance there is tends to the contrary.

But quite apart from the inevitable partisanship which favors such travesties on ordinary political morality, and even more at the bottom of the trouble, lies the vicious system required by the Constitution, of taking the House vote on these 2ņēģēmēņņ2ņēmētiņģēmēģffiti2m22ti22222222/222/22/§Â2Ò§§\§2ti2m2ūņģ§2§Â§Â2Ò2Â?§§\22\/22/2ẸŻ Żņ2 lion inhabitants or less absolute equality with such mighty modern complexes as California, New York, Pennsylvania and Illinois !

Of course there is no doubt, since it is a matter of history, and the sine qua non of the adoption of the Constitution in the first place, that the framers of the (lonstitution did wish to weight the scales slightly to the advantage of the smaller states; which they did by providing equal representation in the United States Senate and consequently somewhat greater weight in the electoral college. Moreover it is impossible to believe that they did not see that they were giving an added advantage to the smaller states in providing that the House should vote by states rather than by total members of the House They certainly did realize this but did not attach too much importance to it. because, in that era, the disparity in the size of the states was not too pro

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