# Myth of the Tyranny of the Majority

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The idea of a "tyranny of the majority" is an old one, going back at least as far as Plato. Many libertarian and Objectivist thinkers simply accept that a government by majority rule would necessarily lead to the expropriation of the productive people in society. As far as I know, no formal argument has been presented to justify the idea.

I propose that direct democracy is (theoretically, at least) the best possible defender of individual rights.

Suppose that we have three people, A, B, and C. Each year, someone proposes a tax rate, all of them vote on it, and everyone gets an equal share of the revenue generated. Additionally, we suppose that A is a "producer". What this means is that he can allocate his time between labor and leisure. Specifically, he can choose a level of leisure l between 0 and 1. Therefore he contributes (1 - l) units of effort towards economic activity. The tax rate is r, and so government revenue R is given by R = r(1 - l). A's retained level of income given a tax rate r is thus, y = (1 - r)(1 - l). Each player's utility function is V(l, y) = l^(1/2) + y^(1/2), where l is the level of leisure and y is the amount of income for that year. Basically, it means that players like leisure and cash about equally, and the more they have of any of the two, the happier they are, though the more they already have, the lower the marginal benefit for each additional unit of that good. It should be noted that B and C always produce 1 unit of leisure and never do any work. We also assume that A's leisure level depends only on the tax rate, l = l( r ).

With this information, we can calculate the revenue maximizing tax rate. Plugging y into A's utility function and taking the derivative with respect to l with a given tax rate r, and finding the maximum, we get A's optimal choice of leisure for a given tax rate which is given by l* = 1/(2-r). From here, we can plug A's optimal leisure choice for a given tax rate into the government revenue equation, take the derivative with respect to r, and then find the revenue maximizing tax rate which is about 58.6% (ouch).

The logic here is simple. When the tax rate is 0%, A spends l* = 1/(2-0) = 1/2 his time on leisure and the other half working. When the tax rate is 100%, A spends l* = 1/(2-1) = 1/1 = 1 (i.e. all) of his time on leisure, since working doesn't do him any good because it all gets taxed away anyway. In between these two extremes is the tax rate at which the government gets the most out of A, that is, they tax him as much as they can without forcing him to become unproductive. At a tax rate of 58.6%, A spends l* = 1/(2-0.586) = 70.7% of his time on leisure and 29.3% working.

To make things easier for the rest of the analysis, we assume that A can always produce some fraction of \$1,000,000 depending on how much of his time he spends working. That is, he produces (1 - l) * \$1,000,000. So, at 0%, A produces and keeps \$500,000. At 100%, A produces nothing and the government gets nothing. And at the revenue maximizing rate of 58.6%, A produces \$293,000 a year, the government gets \$171,698 and A gets just \$121,302.

Now suppose that B proposes to C that they implement this plan. Under it, B and C would get \$57,233 each, while A gets \$178,536. This is clearly a better option for B and C, since it's clearly superior to a 0% tax rate where they each get nothing.

At first glance, it certainly seems as if direct democracy rewards the unproductive majority, but let's dig a little deeper.

Suppose that, after B proposes his plan to C, A goes to C and says, "C, if you vote against this bill, I will give you \$57,234". This is better for C than B's proposal, since he gets an extra dollar, but it is also a better deal for A, since he then gets \$442,766. Almost 4 times as much. B, realizing that he's about to be left with \$0, goes to A and says, "All right, look. I'll vote against this bill regardless of C's vote, if you give me just \$57, 233." This is good for B, since \$57,233 is more than \$0, but it's also good for A, since he saves an extra dollar. But now C, realizing he's the one whose about to get screwed, goes to A and offers just \$57,232 for a vote against the bill. And on and on it goes, until either B or C drop the price for their vote to just \$1. At that point, there's no point in going any lower. The bill fails, the tax rate is 0%, A gets \$499,999 while either B or C get only \$1.

However, there is a clever way for A to save the last dollar. Suppose that he makes the following offer to B and C: "If a tax bill is proposed, I will offer \$1 more than what you can expect to gain from the bill to whoever didn't propose it to vote against it." Since both B and C would prefer for the other guy to propose the bill, neither of them ever proposes the bill. And even if one of them does, the bill fails anyway.

Thus, we see that under a system of direct democracy, a politically strategic producer can never be exploited by the unproductive majority.

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Until they shoot him in the back of the head.

Other than that glich, sounds like a great idea.

Thus, y'all need to get out with the peeps more.

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Until they shoot him in the back of the head.

Other than that glich, sounds like a great idea.

Thus, y'all need to get out with the peeps more.

You can make the same argument against any political system.

EDIT: "Screw the constitution! We'll do whatever we want, and if someone doesn't like it, let them enforce it!"

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Until they shoot him in the back of the head.

Other than that glich, sounds like a great idea.

Thus, y'all need to get out with the peeps more.

You can make the same argument against any political system.

EDIT: "Screw the constitution! We'll do whatever we want, and if someone doesn't like it, let them enforce it!"

Correct.

Of course in an anarchistic system there is no Constitution.

anarchy (n.) 1530s, from French anarchie or directly from Medieval Latin anarchia, from Greek anarkhia "lack of a leader, the state of people without a government" (in Athens, used of the Year of Thirty Tyrants, 404 B.C., when there was no archon), noun of state from anarkhos "rulerless," from an- "without" (see an- (1)) + arkhos "leader" (see archon).

Either the State for ever, crushing individual and local life, taking over in all fields of human activity, bringing with it its wars
and its domestic struggles for power, its palace revolutions which only replace one tyrant by another, and inevitably at the end of this
development there is ... death! Or the destruction of States, and new life starting again in thousands of centers on the principle of the lively
initiative of the individual and groups and that of free agreement. The choice lies with you! [Prince Peter Kropotkin (1842-1921)]

[/indent]

Allways lovin me some Kropotkin...

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Correct.

Of course in an anarchistic system there is no Constitution.

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"No formal argument". (heh) "The logic here is simple". (ouch)

Mathematics (if accurate, I wouldn't know) it seems, can prove anything you like, justifying simple, old-fashioned utilitarianism.

What is "leisure", and why? Why are productive individuals, productive?

This is more Game Theory dressed up as reality, SoMad.

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I propose that direct democracy is (theoretically, at least) the best possible defender of individual rights.

Suppose that we have three people, A, B, and C. Each year, someone proposes a tax rate, all of them vote on it, and everyone gets an equal share of the revenue generated.

Naomi,

Taxes are not individual rights.

Michael

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In a repeated game played by a large diverse population, there would certainly be collusion. Furthermore, you'd have to prove that this works the same when there are 3 parasites and 1 producer playing. And 4:1. And 5:1. Etc.

Another thing that you need to factor in is that many people would rather die than work. And many people are unable to produce more than they consume, so to sustain their life, they must vote on some minimum level of redistribution.

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Democracy ~ alone ~ solely depends upon gracious winners and gracious losers.

For the reason of that inherent flaw, it necessitates a self-responsible, principled citizenry - a Supreme Court - a system of checks and balances - all of which would hold an elected political Party to the exact word and meaning of an objective Constitution.

To close the circle, an "objective Constitution" must enshrine individual rights above all, so an electoral majority can never gain the upper hand (or the power of any one group, over another) rendering such a majority meaningless.

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Sweetie, you are eventually going to have to accept that the reality of human nature != mathematics.

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I propose that direct democracy is (theoretically, at least) the best possible defender of individual rights.

Athens had "direct democracy" Consider what happened to Socrates. Also there were three pro Spartan coups in Athens.

The "people" had a love affair with Alcabiades which ultimately lead to Athens' ruination in the Pollipenesian Wars.

Ba'al Chatzaf

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I propose that direct democracy is (theoretically, at least) the best possible defender of individual rights.

Athens had "direct democracy" Consider what happened to Socrates. Also there were three pro Spartan coups in Athens.

The "people" had a love affair with Alcabiades which ultimately lead to Athens' ruination in the Pollipenesian Wars.

After the death of Alexander the great in 323 b.c.e. Aristotle was convinced he had to "leave town" lest he suffer the same fate as Socrates. He did the following year in Megira, his home town.

In both instances Athens was ruled by direct democracy.

Ba'al Chatzaf

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"No formal argument". (heh) "The logic here is simple". (ouch)

Mathematics (if accurate, I wouldn't know) it seems, can prove anything you like, justifying simple, old-fashioned utilitarianism.

What is "leisure", and why? Why are productive individuals, productive?

This is more Game Theory dressed up as reality, SoMad.

If you don't trust mathematics, then I guess it's time to sharpen your math skills?

As for your question, leisure is anything that someone likes to do but that doesn't make any money. Like consumption.

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Naomi,

Taxes are not individual rights.

Michael

Michael,

Naomi

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In a repeated game played by a large diverse population, there would certainly be collusion.

Can you expand on that? Collusion among who and for what?

Furthermore, you'd have to prove that this works the same when there are 3 parasites and 1 producer playing. And 4:1. And 5:1. Etc.

I don't see why it wouldn't. If there were 1000 parasites and 1 producer, then at the revenue maximizing tax rate, the parasites get \$172 each. Therefore, in order to get a majority, A needs to offer 500 of them \$173 each, which would cost about \$86,500, which is still less than the \$500,000 that A could produce at a 0% tax rate, so he can definitely afford it. Even in the case of a million parasites each of them can get only \$0.17 from redistribution, and the bribe costs A \$0.18*500,000 = \$90,000. A can afford the bribe as long as the number of parasites is less than or equal to 828,803 if money is only divisible to a dollar amount. If money can be divided into cents, then A can afford the bribe for 82,830,201 parasites. But \$171,698 spread out over 82,830,202 people is much less than 1 cent, so at that point, the parasites wouldn't even bother.

Another thing that you need to factor in is that many people would rather die than work. And many people are unable to produce more than they consume, so to sustain their life, they must vote on some minimum level of redistribution.

Or, they can rely on charity from A.

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Sweetie, you are eventually going to have to accept that the reality of human nature != mathematics.

I think we've had this discussion before. Please note that I pointed out the theoretical nature of my argument in my OP. Even if my model isn't a perfect representation of reality ,or even a good one, you have to admit that it presents possibilities that I'm pretty sure were never considered before.

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I propose that direct democracy is (theoretically, at least) the best possible defender of individual rights.

Athens had "direct democracy" Consider what happened to Socrates. Also there were three pro Spartan coups in Athens.

The "people" had a love affair with Alcabiades which ultimately lead to Athens' ruination in the Pollipenesian Wars.

Ba'al Chatzaf

Athens had elections of officials by sortition. That is very very different from what I'm talking about here.

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Naomi,

Taxes are not individual rights.

Michael

Michael,

Naomi

Naomi,

Let me try again.

Taxes are violations of individual rights.

If you wanted to say: "I propose that direct democracy is (theoretically, at least) the best possible defender of plunder," I might agree (or might not) if I were interested in distributing plunder.

But I won't ever agree that this is defending individual rights.

Michael

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Naomi,

Let me try again.

Taxes are violations of individual rights.

If you wanted to say: "I propose that direct democracy is (theoretically, at least) the best possible defender of plunder," I might agree (or might not) if I were interested in distributing plunder.

But I won't ever agree that this is defending individual rights.

Michael

Even if it results in the perfect protection of individual rights?

You can't just go on a mountaintop and proclaim "Thou shalt not tax thy neighbor" (or write it on a piece of paper) and expect everyone to obey. You have to structure political institutions in such a way that no one has an incentive to actually tax anyone else.

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Naomi,

Let me try again.

Taxes are violations of individual rights.

If you wanted to say: "I propose that direct democracy is (theoretically, at least) the best possible defender of plunder," I might agree (or might not) if I were interested in distributing plunder.

But I won't ever agree that this is defending individual rights.

Michael

Even if it results in the perfect protection of individual rights?

You can't just go on a mountaintop and proclaim "Thou shalt not tax thy neighbor" (or write it on a piece of paper) and expect everyone to obey. You have to structure political institutions in such a way that no one has an incentive to actually tax anyone else.

Naomi,

My perspective is that I don't have to do anything to structure you.

I think you've already got that covered.

I don't want you structuring me, either.

I don't need "incentives" for this.

Michael

EDIT: btw - I don't need to go to a mountaintop. I can go to a Convention of States when it finally happens (which it will).

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I think you can expect a lot, but you do have to, sometimes begrudgingly except what is. As to theory of govt/politics and designing a more perfect one, majority rule as a principle doesn't 'jive' with what is to be expected from human nature thus far exhibited. Another problem is what to do with or how to change what is currently in place.

The maths you gave , to me , suggest in principle the way spending/taxing was to be handled in the US Constitution, the money bills must originate in the House ,the closest approximation to 'democractic 'rule. I think the Constitution and the principles it comes from and should stand for are a good if not the best template so far.

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Naomi, The bribe doesn't work when the votes are anonymous. So people will agree to the bride and then vote a liar's vote.

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Naomi, The bribe doesn't work when the votes are anonymous. So people will agree to the bride and then vote a liar's vote.

Who said the votes are anonymous?

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NOW, you're talking.

Take it further - not only, "...no one has an incentive to actually tax anyone else".

How about, "No one would have a need to actually tax..."?

More, "One would find it abhorrent for another to be taxed on his behalf"...?

Then, we can remove the "You", in "You have to structure political institutions..."

- because the structure is already determined, by the rationally selfish individual.

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Naomi,

My perspective is that I don't have to do anything to structure you.

I think you've already got that covered.

I don't want you structuring me, either.

I don't need "incentives" for this.

Michael

It's not about what you want. It's about doing what is necessary to defend individual rights.

EDIT: btw - I don't need to go to a mountaintop. I can go to a Convention of States when it finally happens (which it will).

I wouldn't hold my breath.