How to make the wishes of each person count equally in a social choice problem is a very difficult problem. But sometimes things are skewed far enough in a certain direction that it is clear the opposite direction leads to greater equality in public decision-making. One way to tell might be to think of the hypothetical experiment asking the individuals in two groups in a society whether they would be willing to exchange the political rights and influence they have for the political rights and influence of the other group. But if two groups are unequal in numbers, then one must specify whether it is the political rights and influence per person in each group or the aggregate political rights and influence of each group.

When political rights and influence per person are unequal between two groups, some might claim that is OK if most decisions must be made by consensus or by large supermajorities. In the Federalist Papers #22, Alexander begs to differ. He argues that the power to veto a decision can easily be just as important as the power to get a decision through a legislature. Nations are beset by shocks that require responses if great harm is to be avoided. If a small minority can veto a response it is difficult to make the decision necessary to avoid the harm.

Moreover, Alexander Hamilton argues that if a small minority can veto a measure, it is easier to bribe enough legislators (or offer them other inducements) for corruption to prevent action. This is true even when it is a foreign power that wants to prevent action.

On bribery and other corrupt inducements to national leaders, Alexander Hamilton makes this interesting point:

An hereditary monarch, though often disposed to sacrifice his subjects to his ambition, has so great a personal interest in the government and in the external glory of the nation, that it is not easy for a foreign power to give him an equivalent for what he would sacrifice by treachery to the state.

There is a broader principle here: if a cohesive group has the power to govern by both pushing through legislation they want and preventing legislation they don’t want, this power is likely valuable enough that it will be hard for a foreign power to bribe them. Two circumstances go away from this case. First, if a group is not cohesive, an individual might be bought off. Second, if a small minority can veto legislation, or otherwise has outsized power in some respects, but not others, then it might be possible to buy off most of that small minority, not just individuals.

(On whether a monarch can be bribed to give foreigners a lot of power, an exception to the principle Alexander Hamilton claims is that a monarch might willingly sign a document giving foreigners power over the monarch’s country, thinking to not deliver on the promise of power to foreigners. In this, the monarch might misjudge how easy it is not to deliver on that promise.)

I have the full text below of Alexander Hamiltons arguments in these regards in the Federalist Papers #22. (I moved a footnote into square brackets within the main text at one point.)

The right of equal suffrage among the States is another exceptionable part of the Confederation. Every idea of proportion and every rule of fair representation conspire to condemn a principle, which gives to Rhode Island an equal weight in the scale of power with Massachusetts, or Connecticut, or New York; and to Deleware an equal voice in the national deliberations with Pennsylvania, or Virginia, or North Carolina. Its operation contradicts the fundamental maxim of republican government, which requires that the sense of the majority should prevail. Sophistry may reply, that sovereigns are equal, and that a majority of the votes of the States will be a majority of confederated America. But this kind of logical legerdemain will never counteract the plain suggestions of justice and common-sense. It may happen that this majority of States is a small minority of the people of America [New Hampshire, Rhode Island, New Jersey, Delaware, Georgia, South Carolina, and Maryland are a majority of the whole number of the States, but they do not contain one third of the people.]; and two thirds of the people of America could not long be persuaded, upon the credit of artificial distinctions and syllogistic subtleties, to submit their interests to the management and disposal of one third. The larger States would after a while revolt from the idea of receiving the law from the smaller. To acquiesce in such a privation of their due importance in the political scale, would be not merely to be insensible to the love of power, but even to sacrifice the desire of equality. It is neither rational to expect the first, nor just to require the last. The smaller States, considering how peculiarly their safety and welfare depend on union, ought readily to renounce a pretension which, if not relinquished, would prove fatal to its duration.

It may be objected to this, that not seven but nine States, or two thirds of the whole number, must consent to the most important resolutions; and it may be thence inferred that nine States would always comprehend a majority of the Union. But this does not obviate the impropriety of an equal vote between States of the most unequal dimensions and populousness; nor is the inference accurate in point of fact; for we can enumerate nine States which contain less than a majority of the people 4; and it is constitutionally possible that these nine may give the vote. Besides, there are matters of considerable moment determinable by a bare majority; and there are others, concerning which doubts have been entertained, which, if interpreted in favor of the sufficiency of a vote of seven States, would extend its operation to interests of the first magnitude. In addition to this, it is to be observed that there is a probability of an increase in the number of States, and no provision for a proportional augmentation of the ratio of votes.

But this is not all: what at first sight may seem a remedy, is, in reality, a poison. To give a minority a negative upon the majority (which is always the case where more than a majority is requisite to a decision), is, in its tendency, to subject the sense of the greater number to that of the lesser. Congress, from the nonattendance of a few States, have been frequently in the situation of a Polish diet, where a single VOTE has been sufficient to put a stop to all their movements. A sixtieth part of the Union, which is about the proportion of Delaware and Rhode Island, has several times been able to oppose an entire bar to its operations. This is one of those refinements which, in practice, has an effect the reverse of what is expected from it in theory. The necessity of unanimity in public bodies, or of something approaching towards it, has been founded upon a supposition that it would contribute to security. But its real operation is to embarrass the administration, to destroy the energy of the government, and to substitute the pleasure, caprice, or artifices of an insignificant, turbulent, or corrupt junto, to the regular deliberations and decisions of a respectable majority. In those emergencies of a nation, in which the goodness or badness, the weakness or strength of its government, is of the greatest importance, there is commonly a necessity for action. The public business must, in some way or other, go forward. If a pertinacious minority can control the opinion of a majority, respecting the best mode of conducting it, the majority, in order that something may be done, must conform to the views of the minority; and thus the sense of the smaller number will overrule that of the greater, and give a tone to the national proceedings. Hence, tedious delays; continual negotiation and intrigue; contemptible compromises of the public good. And yet, in such a system, it is even happy when such compromises can take place: for upon some occasions things will not admit of accommodation; and then the measures of government must be injuriously suspended, or fatally defeated. It is often, by the impracticability of obtaining the concurrence of the necessary number of votes, kept in a state of inaction. Its situation must always savor of weakness, sometimes border upon anarchy.

It is not difficult to discover, that a principle of this kind gives greater scope to foreign corruption, as well as to domestic faction, than that which permits the sense of the majority to decide; though the contrary of this has been presumed. The mistake has proceeded from not attending with due care to the mischiefs that may be occasioned by obstructing the progress of government at certain critical seasons. When the concurrence of a large number is required by the Constitution to the doing of any national act, we are apt to rest satisfied that all is safe, because nothing improper will be likely TO BE DONE, but we forget how much good may be prevented, and how much ill may be produced, by the power of hindering the doing what may be necessary, and of keeping affairs in the same unfavorable posture in which they may happen to stand at particular periods.

Suppose, for instance, we were engaged in a war, in conjunction with one foreign nation, against another. Suppose the necessity of our situation demanded peace, and the interest or ambition of our ally led him to seek the prosecution of the war, with views that might justify us in making separate terms. In such a state of things, this ally of ours would evidently find it much easier, by his bribes and intrigues, to tie up the hands of government from making peace, where two thirds of all the votes were requisite to that object, than where a simple majority would suffice. In the first case, he would have to corrupt a smaller number; in the last, a greater number. Upon the same principle, it would be much easier for a foreign power with which we were at war to perplex our councils and embarrass our exertions. And, in a commercial view, we may be subjected to similar inconveniences. A nation, with which we might have a treaty of commerce, could with much greater facility prevent our forming a connection with her competitor in trade, though such a connection should be ever so beneficial to ourselves.

Evils of this description ought not to be regarded as imaginary. One of the weak sides of republics, among their numerous advantages, is that they afford too easy an inlet to foreign corruption. An hereditary monarch, though often disposed to sacrifice his subjects to his ambition, has so great a personal interest in the government and in the external glory of the nation, that it is not easy for a foreign power to give him an equivalent for what he would sacrifice by treachery to the state. The world has accordingly been witness to few examples of this species of royal prostitution, though there have been abundant specimens of every other kind.

In republics, persons elevated from the mass of the community, by the suffrages of their fellow-citizens, to stations of great pre-eminence and power, may find compensations for betraying their trust, which, to any but minds animated and guided by superior virtue, may appear to exceed the proportion of interest they have in the common stock, and to overbalance the obligations of duty. Hence it is that history furnishes us with so many mortifying examples of the prevalency of foreign corruption in republican governments. How much this contributed to the ruin of the ancient commonwealths has been already delineated. It is well known that the deputies of the United Provinces have, in various instances, been purchased by the emissaries of the neighboring kingdoms. The Earl of Chesterfield (if my memory serves me right), in a letter to his court, intimates that his success in an important negotiation must depend on his obtaining a major's commission for one of those deputies. And in Sweden the parties were alternately bought by France and England in so barefaced and notorious a manner that it excited universal disgust in the nation, and was a principal cause that the most limited monarch in Europe, in a single day, without tumult, violence, or opposition, became one of the most absolute and uncontrolled.

Here are links to my other posts on The Federalist Papers so far:

• The Federalist Papers #1: Alexander Hamilton's Plea for Reasoned Debate

• The Federalist Papers #2 A: John Jay on the Idea of America

• The Federalist Papers #2 B: You Trusted the Continental Congress; Trust the Constitutional Convention

• The Federalist Papers #3: United, the 13 States are Less Likely to Stumble into War

• The Federalist Papers #4 A: The States Must Be Prepared to Defend against Aggression by Other Nations

• The Federalist Papers #4 B: National Defense Will Be Stronger if the States are United

• The Federalist Papers #5: Unless United, the States Will Be at Each Others' Throats

• The Federalist Papers #6 A: Alexander Hamilton on the Many Human Motives for War

• The Federalist Papers #6 B: Commercial Republics Also Start Wars with Their Neighbors—Alexander Hamilton

• The Federalist Papers #7 A: Divided, the States Would Fall into Territorial Disputes Likely to Lead to War Between the States—Alexander Hamilton

• The Federalist Papers #7 B: Without Union, Economic Disagreements Would Drive the States to Conflict with One Another—Alexander Hamilton

• The Federalist Papers #8: Without Union, the States Would Either Be Subject to Devastating Wars with Each Other or Would Have Liberty Endangered by their Own Standing Armies—Alexander Hamilton

• The Federalist Papers #9 A: There Has Been Technological Progress in Practical Principles of Republican Government—Alexander Hamilton

• The Federalist Papers #9 B: A Large Confederation May Be More Politically Stable Than a Small Nation—Alexander Hamilton Cites Montesquieu

• The Federalist Papers #10 A: Conflicts Arising from Differences of Opinion Are an Inevitable Accompaniment of Liberty—James Madison

• The Federalist Papers #10 B: The Larger the Republic, the Easier It is to Find Thoughtful Legislators and the Harder It is to Put Together a Majority to do Unjust Things—James Madison

• The Federalist Papers #11 A: United, the States Can Get a Better Trade Deal—Alexander Hamilton

• The Federalist Papers #11 B: Union Will Make Possible a Strong Navy, Allowing America to Chart Its Own Destiny—Alexander Hamilton

• The Federalist Papers #12: Union Makes it Much Easier to Get Tariff Revenue—Alexander Hamilton

• The Federalist Papers #13: Alexander Hamilton on Increasing Returns to Scale in National Government

• The Federalist Papers #14: A Republic Can Be Geographically Large—James Madison

• The Federalist Papers #15: A Government, to be Worthy of the Name, Must Govern Its Citizens, Not Just Its Subordinate Jurisdictions—Alexander Hamilton

• The Federalist Papers #16: Authority of the Federal Government Directly over Individuals Means States Can Only Thwart the Federal Government by Active and Obvious Resistance—Alexander Hamilton

• The Federalist Papers #17: Three Levels of Federal Power

• The Federalist Papers #18: Alexander Hamilton and James Madison Point to the Weakness of Confederations of Cities in Ancient Greece to Argue for a Strong Federal Government

• The Federalist Papers #19: The Weakness of the German Empire, Poland and Switzerland up to the 18th Century is Evidence for the Weakness of Confederations—Alexander Hamilton and James Madison

• The Federalist Papers #20: The Weakness of the United Netherlands up to the 18th Century is Evidence for the Weakness of Confederations—Alexander Hamilton and James Madison

• The Federalist Papers #21 A: Constitutions Need to be Enforced—Alexander Hamilton

• The Federalist Papers #21 B: Alexander Hamilton Complains of the Lack of a Measure Such as GDP Suitable for Apportioning Taxes to the States

• The Federalist Papers #22 A: The Articles of Confederation Lead to Uncoordinated Trade Policy and Military Free-Riding—Alexander Hamilton