our, or perhaps any country's, history, it is not surprising that their dispositions have worked so well. That they have, in fact, worked suggests that their devices are sound in practice, as well as in theory. It seems more reasonable, therefore, to regard the present influence of large states as minimal, rather than excessive. "It thwarts the development of the two-party system in 'sure' states." This is true of the present system, but not of natural voting. At present, the number of electoral votes assigned to any state is fixed, independent of the number of ballots cast within it. Under natural voting, a minority voter in a "sure" state can still make his wishes felt and punish the candidate carrying his state to the extent of the one vote (his own) that he denies to him. This encourages confident candidates in unbalanced states to draw closer to alienated minorities and, by closing that gap, to facilitate the establishment of a moderate opposition. At present, there is no possible advantage to such conciliation on the part of a sure winner. Under district plans, there is none, and raw or proportional plans actually encourage the suppression of minority votes in such states.

"It magnifies both the temptation for and the effect of vote fraud in closely contested pivotal states and subjects the results in whole states to vagaries of accidents of nature."

If a system responds to individual votes, it can also respond to fraud. The presence of this temptation for those so disposed might well be thought of as a testimony to the high value of the individual vote under the present system. Surely, it would not be counted a virtue in a currency that it was not worth counterfeiting. Similarly, the fear of counterfeiters should not drive us to debase our voting system.

"It vests in minority and pressure groups unwarranted power in states where the outcome is in doubt."

It should be said first that in states where the outcome is not in doubt, no voter enjoys any voting power whatever. Further, if voters have no power in states where the result is uncertain, they clearly have no power anywhere. In the Jeffersonian spirit, therefore, individual voters should have significant voting power and it will surely be, if anywhere, in the close states. Moreover, it is very difficult to give individual voters the power demanded by Jeffersonian principles, while denying it to small groups of those same voters. Minorities have no special rights under the Constitution and American tradition except what they derive from the individuals composing them. [6b] The honest exercise of an individual's franchise in protection of his interests and rights ought not too readily be called "unwarranted".

Since Jefferson's time, a majority of Constitutional amendments have sought to maintain, protect, expand, and increase the effect of the popular vote. Natural voting is in this tradition, but every other proposed reform, in at least some respect, runs counter to it.

THE DETAILS OF THE PROPOSED SYSTEM, AND HOW IT RESOLVES DEADLOCKS Natural voting increases voting power by keeping the present leverage, by extending some of it to unbalanced states, and by prolonging its influence in deadlock situations.

On every state's presidential ballot, there will be, in addition to the candidate's names, a line for "No Candidate". Votes cast for any candidate will go to the one who ultimately carries the state; those cast for "No Candidate" will be tabulated and published, but they will not count.

Suppose, for example, that candidate A polled 3.2 million votes, candidate B 3.4 million, and candidate C 400,000, with 1 million ballots marked for "No Candidate." In that case, candidate B would receive credit for 7 million votes, plus the uniform bonus, computed on the total national popular vote and discussed below.

The "No Candidate" option makes the political parties more responsive to individual preferences. Where before, parties needed only provide a candidate calculated to carry a state, they must, under natural voting, take account, in addition, of the enthusiasm he will generate. The individual voter has a far more delicate control of an election in which his vote makes one vote difference in the final result, than he has over a census-based election.

This increased control will tend to increase participation in unbalanced states where, until now, individual votes had no influence whatever over the final national result. Powerless minority party voters can threaten to vote "No Candidate" and gain concessions for their point-of-view from the majority party which

is anxious to maintain its national influence by a large contribution to the national vote. Majority party voters in those states, on the other hand, will have to be enthusiastically wooed by their candidate to ensure that they will actually vote. Under the present, census-based, system, one-party states are often avoided by both candidates. Finally, alienated voters who presently do not vote at all will have the opportunity to make themselves visible, and their moral and indirect influence, felt. Not only will their numbers be exhibited to the realistic leaders of both major parties, their participation in voting for non-presidential office will also be increased.

Last, the "No Candidate" option tends to strengthen the two-party system. At present, protest votes for symbolic candidacies have no effect on presidential elections beyond their presumed absence from the totals of the major candidates. Under natural voting, however, these votes will appear in the total of the candidate carrying the state. This encourages a prospective protest voter rather to choose between the major contenders or to vote "No Candidate" than to vote for a third-party candidate and have his vote go to the candidate he likes least. This discourages splinter candidacies and promotes national, responsible political parties.

In these respects, natural voting is different from, and an improvement on, the present system. In all other ways, it is functionally identical. The successful federal device of providing fixed electoral bonuses to all states, irrespective of size, is retained and held at the present level. Presently, bonus votes (2 electoral votes per state) make up 102/538 of all electoral votes, or 102/436 of those distributed according to numbers. Under natural voting, the number of votes distributed according to numbers is simply the number of popular votes. We make, therefore, the number of bonus votes equal to 102/436 of the total national popular vote, and distribute them equally to all the states. For example, approximately 70 million popular votes were cast in the election of 1968. Each state then, would receive a bonus of 2/436 × 70,000,000 votes in addition to its total popular vote. In this case the bonus would have been 320,000 votes, since the precise number (321,100 based on 70 million) would be rounded, in every case, to the nearest 10,000.

For comparison, let us take the results of the national elections of 1968 in which, exceedingly roughly speaking, 70 million votes were divided among the three leading candidates. 30, 30, and 10 million. Close as the raw popular vote was in percentage, it did not yield under our system, a close election. Under natural voting, this election would have been even less close. The 70 million votes would have divided into pieces of 40, 26, and 4 million. Further, the winning candidate carried 32 states, to 14, and 5, respectively, for his opponents. Adding a bonus of 320,000 for each state carried, the electoral votes under natural voting would have divided, again very roughly, 50 to 30 to 5 million. Scaled to the present number of electoral votes, the distribution would be (316, 190, 32) as against (302, 191, 45), the actual electoral count under the present system. The differences in the two counts reflect the smaller relative turnouts in the states carried by the third-party candidate. Still, the differences are small, as we expected.

Deadlocks would be handled according to the same general principles as the elections themselves. They should be decided, except in extremity, by direct appeal to the election results in detail. The system is, in order of importance, direct, popular, leveraged, compensated and hedged. In deadlocks, therefore, we remove these properties, one by one, starting with the least important, and stopping when the actual results would elect a president with the system we have left. If that fails, we eliminate the low man's electoral votes and, starting from the beginning again, try to choose a president according to the actual results.

Suppose for example, we have an election in which no candidate receives a majority of the natural electoral votes. In that case we remove the compensation (i.e. the bonus votes given to all the states) that is usually a part of the system. (Hedging is probably a less important feature, but there is no way, in counting votes to remove hedging. Its influence is felt entirely before the election.) Thus, each candidate still in the running has a certain number of electoral votes, but all the state bonuses (320,000 votes per state in the example above) have been removed from his count. At that point there may be a candidate who has a majority of the votes remaining. If not, we remove leverage from our system and look for a candidate with a majority of the raw popular vote. If these devices fail to provide a candidate with a majority, we remove the lowest candidate and try again.

Under this system, a voter gains leverage in return for the risk of having hi vote count for the opposition if his candidate does not poll highest in the state Supporters of a candidate who has carried a state, therefore, have taken their risks and won. Thus, their votes should never count in support of the opposition. even in resolving a deadlock. Rather, they would be marked for "No Candidate”. In removing a lowest candidate in the process of resolving an electoral crisis, we simply treat votes for him in the states in which his popular vote was highest, as "No Candidate" votes. We assign the remaining electoral votes in that state in the usual way, to the highest candidate in that state who is still in contention. By this same principle, the votes cast in that state for any other lower candidate, will count for the state's ultimate choice, even if or after that candidate has been eliminated.

To summarize, the election results themselves elect the President if any candidate receives a majority of the electoral votes, or of the electoral votes without bonuses, or of the raw popular vote. A crisis is also avoided if, after having treated as votes for "No Candidate" the popular votes cast for an eliminated candidate in a state he originally carried, one of the remaining candidates achieves one of the three kinds of majority. The process of elimination of low candidates simply continues until someone achieves a majority of the remaining votes, or until fewer electoral votes remain unremoved than there were actual popular votes at the start.

To illustrate the operation of this sequence, let us assume that the two leading candidates had exchanged their 1968 totals in California, bringing about a deadlock under the present system. Under natural voting, that would also have brought us very close to indecision with respective electoral vote counts of (42.5, 37.5, 5) million votes. Under the process described above, the next step would be to remove the state bonuses. The totals would then be (33, 33, 4) million votes, still undecided. Last, we would look at the raw popular votes, (30, 30, 10) millions, without finding a majority. This forces us to eliminate the lowest candidate. He had carried 5 states in which he had polled 2.3 million votes, roughly a fourth of his total raw vote. Those 2.3 million votes are then treated as "No Candidate" ballots and the remaining votes in the 5 states, reassigned. Since the second candidate would have led in four of these five states, he would have had a majority of the uneliminated electoral votes. We need only check that the fraction of electoral votes remaining is great enough to satisfy the restriction. Of the roughly 85 million original electoral votes, we must have at least 70 million (the number of raw popular votes cast) left in order to elect the president. In this hypothetical case, we have eliminated only 2.3 million votes, and the system succeeds in avoiding recourse to any further alternative. If this process fails to find an appropriate majority at some stage, the choice is left to the House of Representatives following the same principles as have guided the process thus far.

The decision reasonably falls, finally, on the Representatives who have been elected at the same election as the president they are to choose. For that reason, if a Senator is elected from any state at such a deadlocked election, he would take part in the deliberations of his state's congressional delegation and speak for the bonus votes of his state.

The House takes up the problem at the point where the election results failed. That is, it chooses among the candidates that had not been eliminated in the earlier phase, Its mode of voting will be precisely parallel to that of the normal election itself. States vote, at first, as units commanding all their natural electoral votes, then without their bonuses. If no candidate receives a majority, the Representatives vote as individuals. Should this fail, the candidate with the fewest votes in the first of these three tests is eliminated, and the balloting repeats the cycle with those remaining. This preserves the order of importance of the features of voting: it eliminates compensation, then leverage, but remains direct and popular to the end.

It is appropriate to compare this resistance to deadlock with that of other methods. The present method, in the election of 1968, is believed to have come very close to impasse in that the switch of a single state could have brought it about. The raw direct popular vote proposal of the American Bar Association, in which particular care was paid to the problem of deadlock, would, on the results of 1968, have found itself close to difficulty: it requires a minimum of 40 percent of the raw vote for victory, whereas the winning candidate had only about 43.5 percent. The entrance of a fourth party candidate might well have

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pressed such an arrangement very hard, without changing the results in the electoral college by a single vote. By contrast, the effect of non-major parties on the 1968 results would have to have been more than six times larger than they actually were to precipitate such a crisis under natural voting.

A FORMAL DESCRIPTION OF THE MAJOR ELECTORAL REFORM PROPOSALS The present system has been so successful and popular that proposals to reform it, however different they might be in operation and success, resemble it closely. It is possible, therefore, to describe all the major proposals in terms of a very few controversial features of the present system. That method simply operates on a dual base of popular elections and state influence. Voters are grouped, by states, in winner-take-all districts governed by majority vote. In addition, the candidate carrying any state receives, aside from the votes allotted that state aecording to size, a fixed bonus of votes that is the same for every state, regardless of size. Last, the size-dependent share of any state is determined by its census population.

The present system is also indirect, in that the final choice is placed in the hands of "electors," and is not directly determined by the outcome of the popular voting. It is widely agreed that the president should be chosen directly by the election returns. We discuss therefore, only the remaining points of difference between the reform proposals and the present system. They involve exactly three points. How, if at all, should voters be grouped in winner-take-all districts (by state, by congressional district or by individual)? Second, should candidates receive a bonus for polling highest in each state? Third, should the number of votes assigned to a state be based, primarily, on its census population, or on its actual total of presidential votes cast? There are only 18 possible combinations of answers to these questions, 3 of which have appeared in major reform proposals, 1 is now in effect, and 1 is proposed here. They are summarized in the table below:

The point least in dispute is that our voting system should be popularly based. The trend of public polls indicates large popular support in that direction. Moreover, census-based systems promote the possibility of electing an outvoted president, without conferring any strategic compensating advantage. This reduces the field to direct, popularly-based elections, of which there are nine different kinds. Among district sizes we have the three choices listed above, and there are three different positions on the division of state bonuses. We can combine any pair of these to form a direct, popular system.

The voting power equation suggests that large states have greater voting power than do small, even per capita. The electoral bonus tends to equalize states' influences in the national election, per capita. (Note that we are not discussing the separate question of individual voting powers in the various states. Rather we are applying the voting power equation to the case of 51 states with varying numbers of electoral votes.) The question is nearly academic, however, since the electoral bonuses are regarded as fundamental by every small state, and the absolute support of the small states is required to ratify any constitutional amendment.

Any new voting system adopted, therefore, is likely to provide state bonuses, and moreover, to distribute them according to the winner-take-all principle. That method has been, for many years, the favorite of the states, all of whom could have chosen, under the Constitution, any method they liked. At present no other method has been adopted by any state, and it is unlikely that a constitutional amendment could be passed that enforced a different disposition. The effect of single ticket, or winner-take-all, methods is to increase the marginal value, to the candidate, of carrying the state. With it, the state's bargaining power, and

the power of state officials increase. There is, therefore, only the size of presidential voting district to be settled.

Congressional districts can, on technical grounds, be set aside. Apart from the temptations presented by gerrymandering, congressional districts manifest another defect; they tend to be homogeneous, rather than balanced, and unbalance is, according to the voting power equation, anathema to individual voting power. Half the Congressmen elected in 1968, for example, carried 64 or more percent of the votes cast in their districts. The median state was carried with 50 percent of the vote (although this was, because of the presence of a third-party candidate, an unusually low figure) in the presidential election.

Without referring to the voting power equation, we can see that the individual has greater voting power when he votes with the other voters of his state, on a winner-take-all basis, than he would voting alone. Peirce [7] has given an extensive list of presidential elections in which the switches of relatively few votes in close states would have tipped the elections in favor of the minority candidate. Stated in a different way, small numbers of votes can, by systematic shifts, turn elections where they could not turn popular totals, when votes are grouped by state. This, of course, magnifies the impact of the individual vote and makes it more of a factor in the election. In fact, candidates very rarely win without a plurality of the popular vote, even though it is technically possible. This is because candidates understand the possibly disastrous effect that could be generated by minority votes in balanced states who felt their interests were threatened. Without some such tendency, close states tend to split according to coin-tossing statistics and elect the more popular candidate. If the minority candidate were elected, it would not mean that the minority had chosen him, but rather that there was a substantial vote against his opponent. In the sense of Jeffersonian democracy and electoral systems then, the opposite of majority rule is not minority rule; it is protective minority veto.

We conclude from this that states form the best voting district among those proposed, and that, from the arguments above, each of the properties of natural voting is either dictated by practical or historical considerations, or else deducibly best by arguments based on Jeffersonian principles. Since, historically, our present system has been nearly perfectly Jacksonian, the natural system (which is more Jacksonian) is attractive from both major democratic points-ofview, and has either a practical or a Jeffersonian advantage over any other direct voting system using seriously proposed electoral devices.

THE NUMERICS OF DEADLOCK AND NATURAL VOTING

Deadlocks are not actually impossible under voting, but they require circumstances that have never been remotely approached in our history. It takes a mathematical minimum of approximately 106 electoral votes and sixteen million popular votes (based on 1968 figures) to enable a third-party candidate to throw the election to the House of Representatives, under natural voting. A candidate could get a third, in fact, of all the electoral votes and still not force a deadlock under that system. To emphasize, if a third party candidate gets less than 106 electoral votes, there is no chance whatever of a deadlock. If he gets more, there may be a deadlock, though probably not. Only a third-party candidate who does fully as well as a major candidate, in the many electoral respects measured by natural voting, can expect to cause a deadlock. It is worth noting, too, that in roughly half the elections of this century, one major party candidate gathered fewer than the minimum number of electoral votes needed to make a deadlock possible. Stated positively, if a third-party candidate does cause a deadlock under natural voting, he must have done better than half the major party losers in this century. At that point, he is no longer a splinter candidate, and we are no longer dealing with a familiar two-majory-party election.

This performance of natural voting should be compared with raw and present voting procedures. The smallest conceivable vote total that is able to produce deadlock at present is about 25,000. A candidate could carry Alaska with that many votes in a three-way election, and thereby deny either of the other two candidates a majority in our present electoral college.

Under the American Bar Association's raw voting proposal, the minimum third-party vote required to make a deadlock possible would be 14 million, and 21 million would ensure a deadlock. Moreover, if any number of splinter parties