“If we live in a democracy and you don’t use your power to vote…
Shame on us… So what the fuss!
Shame, shame.
Shame shame shamity shame.“
Stevie Wonder, “So What the Fuss” (feat. Prince and En Vogue)

Power, in the broadest sense, is the ability to act according to your will by exerting control over your environment.

The more power you have, the more needs and desires you can fulfill. You use this power every day to claw your way a little higher up Maslow’s hierarchy of needs. You usually get stuck at “eat Cheetos now and for the foreseeable future” on your journey towards self-actualization.

But things get complicated as soon as your environment becomes polluted with other people. Resources are scarce, and this leads to conflicts.

Power over nature can extend to power over people. Your power to eat the last Cheeto disempowers me from eating it.

And I was saving that one, you jerk. It had a funny nub.

Power begets power. The more power you have, the more you can gain.

This concern shapes events from union strikes and Marxist revolutions to interventionist foreign policy and pre-emptive war. We often hear about the need to counterbalance the economic power of a large corporation or the military power of a foreign state. At best, these “balance of power” strategies yield a stalemate of mutual distrust and hair-trigger brinkmanship.

Democracy is intended to circumvent such conflicts by distributing power among the masses. “Empowerment” is regarded as synonymous with voting. The vote is the means by which marginalized groups could break their shackles, have their say, and win back the freedoms that they have lost to the power of others.

But how much power does a vote really bestow?

You Call That “Empowerment?”

Under conditions of scarcity, the exertion of power takes the form of a choice. A choice is an “all or nothing,” “A or B,” binary event. You can have one thing only by giving up another.

A single vote is not a choice; the whole election process results in only one choice.

As an isolated individual, you make 100% of all choices. This doesn’t mean that you are all-powerful, because your available choices are still limited by natural constraints. You can’t walk through walls. But nobody else is around to eat your Cheetos.

Let’s introduce one other person, and empower each of you with an equal vote on all choices. You now only have 50% of the power you previously held. So does Person #2.

Now Person #3 comes strolling in, and because you are both tolerant of immigrants, you and Person #2 vote unanimously to empower Person #3 with an equal vote. This noble choice has knocked all three of you down to 33%.

There is a simple mathematical relationship at work here. The power of any individual’s vote can be calculated as:

(?????????? ?????? ?????)=100%×(1 ?????)/(??? ??????)

Figure 1 shows the hyperbolic curve produced by this function (in Cheeto orange), up to 100 million voters. This is roughly how many US citizens actually vote.

Chart showing Individual Voting Power as a hyperbolic curve up to x=100 million voters, with linear x axis

Figure 1

Well, that doesn’t look like much. It seems to immediately drop from 100% to zero. Huh.

Changing the horizontal axis to a logarithmic scale reveals more detail at the lower end:

Chart showing Individual Voting Power as a hyperbolic curve up to x=100 million voters, with logarithmic x axis

Figure 2

We see the effects of 2 and 3 voters, as discussed above. By moving to the right along the the curve, we can consider increasing population sizes, similar to the “scales framework” discussed in Anarchitecture Podcast’s Foundations Series.

At 10 voters, your voting power is 10%. This could be a small club, sports team, or business. They say that if 10% of a population is passionate about a cause, the others will often follow. So an individual may have some sway at this scale.

At 100 voters, your power drops to 1%. This could be a community group, rural village council, class president, or medium-sized business. 1% already sounds low, but you could form a voting bloc on an issue by canvassing people one at a time. Empowerment at this scale takes some work.

Let’s jump to 10,000 voters. This is somewhere around the median population for a typical U.S. city. You are empowered to 0.01% of the choice for mayor.

0.01 percent. You call that “empowerment?”

I call that “zero.” And that’s at the scale of small town local politics, where “your vote really matters.”

Your coveted vote for President of these United States gives you a whopping 0.000,000,8% of the choice. That’s less than one millionth of one percent of a choice, or 8 nano-choices.

Less, if there’s a good voter turnout.

The margin of error when counting votes is probably a few orders of magnitude higher than this, so that your vote is truly worth zero.

In an election, you have no choice. You are 100% powerless.

Empowerment by Isolation?

There are common stereotypes of the right wing sovereign man or left wing hippie who disconnects from society to live off the land in survivalist fashion. This isolation is an attempt at re-empowerment by moving to the left along the curve, so that his choices are no longer subject to the will of anyone else.

Is this what it takes to empower yourself?

The isolationist has overlooked a key assumption in the chart above. He may throw off the burden of society and move towards 100%. But what does he end up with?

100% of what?

We can more formally define an individual’s power to make his own choices:

(?????????? ?????)= [(????????? ?ℎ?????)]×[(??????? ???? ?ℎ?????)]

The first term represents the total number of choices that are available to an individual at any given time. In the previous section, we assumed a fixed number for this term and ignored it.

Under this isolationist scenario,

(????????? ?ℎ?????)= [(?????????? ?????????? ?????)]

“Individual Production Power” represents the number of choices available as a result of the individual’s skills, knowledge, and real capital goods (tools, machinery, house, etc.)

The second term is the individual’s “Voting Power” as described above, so that we can rewrite Individual Power as:

(?????????? ?????)= [(?????????? ?????????? ?????)]×(1 ?????)/(??? ??????)

The isolationist has restored the second term to 100% by reducing “All Voters” to “1 Voter.” However, his power is limited to what he can produce with his own two hands. He can increase his number of available choices by learning new skills or building capital goods, but he does so without any outside assistance.

He can’t even produce partially hydrogenated soybean oil, let alone an entire Cheeto.

Economic isolationism does not lead to empowerment.

Empowerment by Voting Bloc?

“Disempowerment by Democracy” can be seen in every protest, petition, and political campaign. Each of these strategies is an attempt by a small, powerless group of people to influence a larger group and form a majority voting bloc in hopes of realizing empowerment.

The “Bloc Size,” or number of people in this bloc, replaces “1 Voter” in the numerator:

(???? ?????? ?????)= 100%×(???? ????)/(??? ??????)

Figure 3 shows “Bloc Voting Power” curves for various Bloc Sizes:

Chart showing multiple hyperbolic curves of Bloc Voting Power shifted to the right depending on Bloc Size parameter, logarithmic x axia

Figure 3

If 100% of the people agree with you on everything, then the result is effectively the same as the isolated individual case, where you have 100% control. Here, democracy is superfluous.

If everyone else disagrees with you on everything, then your Bloc Size=1 (orange curve), which is identical to the original curve shown in Figure 2.

Also, you’re probably a libertarian.

Since there are often many like-minded people on a given issue, and a group of like-minded people may be able to convert others, it is possible to achieve one of the curves above, or something in between.

This possibility is the sole reason for belief in “Empowerment by Democracy.”

This idea is typically applied to a group of people assumed to share common interests, such as socioeconomic class, geographic location, culture, gender, or ethnicity. Under an assumption of “identity politics” where votes are cast based on group identity rather than consideration of individual issues, these people can all be counted in a bloc.

Since these are often minority groups, they still need to sway other voters to support their cause in order to win a majority vote.

A nationwide petition with 100,000 signatures is represented by the blue curve. This vital issue is worth 0.1% of the President’s attention.

The green curve shows the power of a “million man march.” This is a massive effort of activism. 1 million people taking a day off from work costs roughly $60 million in lost income (or leisure time). This expense, around 10% of a presidential campaign budget, buys a measly 1% of the result for a federal vote.

If the publicity goes viral, so that each protester wins over 10 apathetic Cheeto-scarfing couch potatoes who usually find protesters annoying, crank that up to… 11%.

It’s something, but is it enough? Is it worth the effort?

The amount of “Individual Bloc Voting Power” that you can exert over a voting bloc is determined by:

(?????????? ???? ?????? ?????) = 100%×(1+[(????????? ??????)])/(??? ??????)

This is the number of people whom you can personally convince to join your bloc, as a proportion of all voters. Out of all of your friends, how many have ever changed their mind about politics because of something you said? One? Ten?

If you miraculously convert 100 friends from “voting against Politician A,” to “voting against Politician B” your Individual Bloc Voting Power for President jumps from 0.000,000,8% (orange curve) to 0.000,08% (red curve).

In a relative sense, that’s certainly something. In an absolute sense, it’s still absolutely nothing.

Add to this the uncertainty that your own efforts may still fail to build a large enough bloc against your opposition, who have formed their own bloc.

This isn’t empowering anyone.

The Scope of Democracy

To avoid complications and present the “best case” scenario for “Empowerment by Democracy,” our analysis here assumes “one man, one vote” direct democracy. We also assume that there is no coercion, corruption, intimidation, bribery, gerrymandering, voter fraud, miscounting, or any of the other shenanigans that plague real world elections.

This is democracy at its theoretical best.

The above charts show how your life would be affected by a “totalitarian democracy,” in which every choice you make is ultimately decided by a referendum.

The scenarios considered above represent extremes, with reality somewhere between the isolated individual case and the totalitarian democracy case.

Let’s assume that only 30% of your choices are affected by democratically decided laws. If this sounds high, compare your total taxes paid (federal, state and local) to your gross income. Then estimate the percentage of your daily activities that are restricted, mandated, or otherwise influenced by various laws, regulations and surveillance. 30% is probably low-balling it.

This means that person #2 would reduce your power by 15% (½ of 30%) to 85%. Person #3 would reduce it to 80%, and so on.

In a large population, your “Amount of Control Over Choices” would asymptotically approach 70%, instead of zero. This function is:

(??????? ???? ?ℎ?????)=(30%×(1 ?????)/(??? ??????))+(70%×(1 ?????)/(1 ?????))

To generalize, where d is defined as the percentage of choices determined by democratic voting:

(??????? ???? ?ℎ?????)=100%−?×(1−(1 ?????)/(??? ??????))

Which simplifies to:

(??????? ???? ?ℎ?????)=(?×(1 ?????)/(??? ??????))+((1−?)×100%)

Figure 4 shows various values of d as separate curves:

Chart showing hyperbolic curves of "Control over Choices" compressed upwards depending on parameter "d"

Figure 4

Proponents of democracy want to increase d so that more decisions are made by voting. This moves the curve down, towards totalitarian democracy (orange curve).

Advocates of small government want to increase Individual Power by reducing the value of d, thus causing the curve to move up towards 100% individual choice (yellow curve).

A lower value of d also decreases the amount of power bestowed by a vote. This is a trade-off between control over your own choices and control over the choices of others. d=30% means that your vote only empowers you to control 30% of other people’s choices, compared to 100% under “totalitarian democracy.”

So here, too, while your Individual Power may be greater, the case for “Empowerment by Democracy” grows thinner.

Empowerment by Markets

In a market, you control 100% of each choice. The choices available to you are limited only by your budget.

Most of these decisions seem less glamorous than weighing in for 0.000,000,8% of the choice to unleash some new national healthcare scheme that promises everyone access to more choices.

But you make hundreds of 100% choices each week, each of which has a direct, immediate, positive impact on your life. Compare that to your uncertain 0.000,000,8% of a choice every 4 years.

Which of these choices are really empowering you?

While less well defined than the democracy curves above, we can construct a similar “empowerment curve” for the market.

Again, we will set the benchmark for an isolated individual at 100%.

A second person introduces a significant leap in possibility and efficiency. Two people can perform tasks that are impossible for one person, such as carrying heavy objects or making babies. They can also specialize according to their individual strengths.

When two people trade goods, the additional gains realized by each party, whether in money or real goods, are profits. These profits incentivize both people to produce more than they need, in order to reap the benefits of trade.

As more people enter the market (perhaps due to all of the baby-making), so do more diverse goods and services. Larger and more complex capital investments become feasible, further increasing the abundance of goods through greater productivity. This, in turn, increases the number of choices available to each individual.

The representative curve of this real profit, or “Market Power,” would likely be some form of logarithmic function. A scaling factor “C” can be used to adjust for the expected marginal contribution of each new person. This can be added to “Individual Production Power” (which is set at 100%) to show Individual Power in a free market, without democracy:

(??????@?????)= ?×log⁡(??? ??????); (????????? ?ℎ?????)= [(?????????? ?????????? ?????)]+[(?????? ?????)]; (????????? ?ℎ?????)=100%+?×log⁡((??? ??????))

A range of possible curves with different values of C are shown in Figures 5 and 6. These both show the same curves, with linear and logarithmic scales on the horizontal axis.

Chart showing logarithmic curves for "Available Choices" depending on Market Scaling Factor (C), linear x axis

Figure 5

Chart showing logarithmic curves for "Available Choices" depending on Market Scaling Factor (C), logarithmic x axis

Figure 6

This logarithmic curve indicates that a new person joining a population of 100 can offer much more to each of those 100 people than a new person joining a population of 100 million can. How much more depends on the value of C.

C=0.0 is the “isolationist” case. The orange curve is flat, with no gains from additional people. An economic isolationist has zero Market Power.

The other curves show possible values that might approximate the real world. For a given economy, C might be determined by factors such as productivity, tax policy, or the total capital stock. Determination of an empirical value of C, if possible, is beyond the scope of this article.

Contrary to democracy, markets increase power for each individual as population increases.

Under democracy, society is a burden. But in a free market, it is the engine that drives empowerment.

The General Theory of Empowerment

All of the above can be combined into a single formula to show the interplay between “Empowerment by Markets” and “Disempowerment by Democracy.”

Let’s call this “The General Theory of Empowerment.”

I feel empowered just saying that. If Keynes could call a bunch of incoherent crackpot ramblings a “General Theory,” then so can I.

Starting from our original definition of Individual Power, we can plug in the various components defined above:

(?????????? ?????)= [(????????? ?ℎ?????)]×[(??????? ???? ?ℎ?????)]; (?????????? ?????)=([(?????????? ?????????? ?????)]+[(?????? ?????)]" " )×[(??????? ???? ?ℎ?????)]

Which finally yields:

(?????????? ?????) =(100%+?×log⁡((??? ??????)))×(100%−?×(1−(1+[(????????? ??????)])/(??? ??????)))

The General Theory of Empowerment

That’s a lot to digest. And your digestive system is already overburdened by that recent onslaught of Cheetos. Let’s look at a chart.

For simplicity, we will assume the following:

  • All people are voters.
  • You haven’t converted any voters to form a bloc, because the effects would likely be negligible.
  • We will arbitrarily choose a fixed value of C and see what happens under various values of d.

This will give an idea of how more or less democracy affects Individual Power within a market economy.

Chart showing Individual Power curves with "C"=0.5, various values of "d"

Figure 7

Curves with more choices determined by voting (high d) ultimately reduce individual power, since the democracy component is dominant. Under “totalitarian democracy” (orange curve) any contributions from the market are crushed.

There is a “break even” point where the curve can cross over 100%, escaping the counterproductive black hole of democracy. The market component counterbalances, then overwhelms, the democracy component. As d is reduced, this occurs at lower population sizes, and the benefits of a large market economy can be realized.

Empower Yourself, and Everyone Else

Politics has it backwards. Elections play an increasingly significant role at larger scales of government, yet just a handful of voters renders your vote worth less than a handful of Cheetos.

Voting gives only the illusion of empowerment. Thinking that you have some measure of control, even a vanishingly small one, you relinquish your choices to the electorate.

You choose to disempower yourself.

Democracy does not empower anyone. It disempowers everyone except for the politicians whose own choices are granted legitimacy by the resulting “popular mandate.” This is one-way empowerment, from the masses to the entrenched elites. Power begets power.

By accepting your powerlessness under democracy, you can focus on real empowerment. You can stop expecting everyone else to make choices for you. You can stop wasting time, energy, and friendships arguing over politics. You can think, learn, speak, create. You can build.

Don’t protest. Produce. Free markets promote two-way empowerment. Through cooperation, investment, and trade, you can empower others. Power begets power.

Empower yourself, and everyone else. Don’t vote.

And lay off the Cheetos, you revolting slob.


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