Paradoxes make good brain candy, in my opinion. As a rough approximation, statements can be deemed a paradox when they provoke the reaction “That can’t be right but I also don’t see how it can be wrong.” W. V. Quine once described how paradoxes can be put into three different categories: veridical, falsidical, and antinomy.
A paradox is veridical when it seems impossible or contradictory but turns out to be true when properly understood. Statistics is full of these kinds of paradoxes. One example is Simpson’s Paradox, which, as Steven Landsburg has explained, can lead to the seemingly paradoxical situation where you can see “median income shoot up in every demographic sector while the overall median remains nearly unchanged.” Russ Roberts has also skillfully unpacked this paradox as well.
The second category is a falsidical paradox. This is a when the paradox is dissolved by understanding why it is actually false. A classic example is Zeno’s argument for why Achilles can never catch up to a tortoise in a race. We instinctively understand the argument must be mistaken—indeed, we know it’s mistaken because we see the supposedly impossible outcome occur in reality all the time. But for centuries nobody could explain what the error was, until mathematicians proved an infinite series can sum up to a finite total.
The third type of paradox is antinomy, which is the category of “wait, are logic and reality broken?” These are paradoxes that remain unsolved. To resolve a paradox is to move it out of antinomy and into the veridical or falsidical spaces.
Lately, I’ve been pondering Condorcet’s paradox in this framework. Very briefly, this describes when majority rule produces a rock-paper-scissors style of result. Individually, I might prefer waffles over French toast, and French toast over pancakes. These preferences will be transitive—since I like waffles more than French toast and I like French toast more than pancakes, I also like waffles more than pancakes. But voting doesn’t necessarily produce transitive outcomes. Among these three options, individuals can rank them in a different order, and voting by majority rule can produce results where waffles beat French toast, French toast beats pancakes, and pancakes beat waffles.
This outcome seems paradoxical. When the majority prefers waffles, the majority prefers pancakes. But when the majority prefers pancakes, the majority prefers French toast. However, when the majority prefers French toast, the majority prefers waffles. How can we use democracy to discern and carry out the will of the majority, when what the majority wants is simultaneously not what the majority wants? We seem stuck in a contradiction.
One way to resolve the seeming contradiction by recognizing there is a fallacy of equivocation. The fallacy of equivocation is when the same word is used throughout an argument but refers to different things at different points in the argument. In this case, we’re using the same word—“the majority”—to refer to partially overlapping but different collections of individuals. Let’s say there are three hundred voters in total. The “majority” that picks waffles is not the same “majority” that picks French toast, and so on. What we actually have are three distinct “majorities”—with apologies to any monetary economists reading this, we can call them M1, M2, and M3. M1 consists of the first and second hundred voters, M2 is made up of the second and third hundred voters, and M3 is the first and third hundred. Now we can reformat our previously paradoxical statements as “M1 prefers waffles, M2 prefers French toast, and M3 prefers pancakes.”
This approach might seem to resolve the logical contradiction, but there are still practical problems on the table. Democracy, we are often told, is justified because it makes the government accountable to the majority. But M1, M2, and M3 can all with equal legitimacy claim to be “the majority,” and they all want incompatible outcomes. How do we resolve this problem, in a way that preserves democratic legitimacy?
The answer to this, in my opinion, is to recognize that the very question is falsidical. To speak of “the will of the majority” or “what we as a society have decided” is to commit a category error. It makes the mistake of applying concepts like decisions, desires, will, and so forth, to a category where they simply don’t apply. It treats “the majority” is though it were a thing that has an active and independent existence, as though “majorities” or “societies” are the kinds of things that are capable of having desires or making choices. But the statement “M1 prefers waffles” is meaningless.
This is because a majority is not a thing that exists. Or, to phrase the point more precisely, the majority does not exist as a thing. A majority is simply a relative form of measurement, not an entity with a real existence that’s capable of having preferences or making choices. “The majority” is real and exists in the same way and in the same sense that velocity exists. That is, things have velocity, but there’s nothing that is velocity. Similarly, a certain number of people or things in various schemas can be defined as “the majority,” but there’s nothing that is “the majority.” To use phrases like “the will of the majority” or “as a society, we have decided such and such” is as fundamentally incoherent as saying “for this experiment, I’m going to need three pounds of velocity.”
And that’s how I see Condorcet’s Paradox. Instead of wondering how it can be the case that what the majority wants is also not what the majority wants or wondering how a democracy can respect “the will of the majority” when there are multiple, equal majorities with incompatible “wills,” we would do better to recognize that the whole premise is ill-formed. Hayek once said, “We shall not grow wiser before we learn that much that we have done was very foolish.” Endlessly searching under the rainbow for “the will of the majority” is a foolish task—because there never was such a thing to start with.
READER COMMENTS
Thomas Hutcheson
Apr 26 2023 at 11:25pm
I do not see that any “resolution” is necessary. Voting systems can produce M1>M2>M3>M1.
nobody.really
Apr 27 2023 at 10:51am
Broadly speaking, people have used two methods for resolving matters that exceed the capacities of individual negotiation: 1) civil war or 2) a ritual that bestows a sense of legitimacy on a public choice. Many societies have adopted elections as this ritual. Elections have the primary advantage of RESOLVING DISPUTES WITHOUT A CIVIL WAR. But people often seek to bolster the case for elections by praising them as an objective mechanism for ascertaining the views of the majority a/k/a public opinion. This matters because, as a first-order approximation, a cause that could muster most people’s support may have a greater opportunity of prevailing in a civil war; in this sense, an election looks like a low-cost proxy for a war.
Some fancy-pants game theorists/economists have noted that, even if you assume that every individual has consistent preferences—consistent in valuing A over B over C, and consistent over time—shifting coalitions of individuals would reveal a majority of voters prefers A over B, a majority of these same voters prefers B over C, and a majority of these same voters prefers C over A.
More practically, how you phrase questions (“question architecture”) can influence people’s decisions. 37% of kids want to spend recess playing boardgames; 32% playing soccer; 31% playing kickball. If you pick based on a plurality of these choices, you go with board games. But if you first ask if kids would like outdoor activities or indoor activities, you’d get a majority picking outdoor activities—and then you could have a vote for which outdoor activity to pursue.
Finally, research reveals the individuals do NOT have consistent preferences—consistent over time, or even consistent among options.
All of this undermines the idea that elections provide an “objective” reflection of the preferences of the majority. This leads to two practical results.
First, Corcoran exhorts us to modify our speaking—and thus, our thinking—when addressing the outcomes of elections. This strikes me as wise and appropriate—except for the other practical result.
Second, because these arguments undermine the objectivity of electoral outcomes, they may tend to undermine people’s inclination to defer to electoral outcomes—and, by default, strengthens people’s inclination to resort to civil war. This strikes me as dangerous.
In a previous thread, we discussed whether the maintenance of society requires people to embrace some amount of myth. Perhaps elections do not have all the objectivity ascribed to them—but perhaps we are better off embracing the idea that they do.
robc
Apr 27 2023 at 1:06pm
That is one option. The other thing it could lead to is that realizing while all election methods have problems, some have more than others. So we could get to your point by going to less problematic methods.
If I was emperor for a day, I would make 3 changes to US election processes…two of which are contradictory!
-All elections are ranked choice instead of plurality.
-For presidential elections, Electoral college votes would be determined by the ME/NE plan (2 EC to statewide winner, 1 each for each district winner). Suddenly there arent battleground states, but battleground districts instead. Before the last few elections with fraud claims abounding, I stated that this method helped with fraud prevention, in that massive fraud in a single location could switch at most 3 EC votes, as opposed to a whole state. I think think that is important, but point out I have been stating this for decades, so I don’t get lumped into some sort of election denier category.
-And contradicting the one above, I would get rid of house districts altogether and each state would select its reps by single transferable vote, which is a form of ranked choice, so not contradicting the first at least. This would make CA awesome, as it would take less than 2% of voters to elect a candidate. CA would be represented by all kinds of people: Libertarians, Greens, Communists, etc. While you might not get your very first choice, everyone would be electing a rep (except for Dems in Wyoming).
nobody.really
Apr 27 2023 at 1:37pm
I like all of those—although I may not fully grasp your third proposal. I think you’re describing one of Lani Guinier’s election reform ideas. Or maybe you’re describing electing Congressmen on an at-large basis (without districts).
I think of Lauren Boebert as an at-large representative—meaning that the authorities have not yet taken her into custody.
robc
Apr 27 2023 at 2:46pm
Yes, at-large districts. I think you would get some regional voting…I would prefer to vote for a local NoCo candidate over a Denver candidate, for example. Or in Boebert’s case, western slope GOPers might prefer to vote for a republican in another part of the state to avoid voting for her, but then again, some front range republicans might vote for her.
The really interesting part would be primaries. To use CO as an example, there are 8 reps, so you get 8 candidates per party to be on the ballot. Selecting those 8 would get interesting. Does the GOP only put 1 or 2 metro Denver residents on the ballot to try to concentrate Denver GOP votes on them? Or go ahead and put 4 on there and figure they will concentrate thru 2nd, 3rd and 4th choices anyway?
Thomas Hutcheson
Apr 27 2023 at 5:37pm
After statehood for Puerto Rico and DC, of course.
nobody.really
Apr 28 2023 at 6:36pm
Emily Litella [a somewhat deaf/senile woman played by Gilda Radner]: … I hear that President Ford wants to make Puerto Rico a steak! … Now, why does he have to make them a steak? I didn’t think those people even liked meat. … Now, let me warn all of you. If you make Puerto Rico a steak, the next thing they’ll want is a baked potato! With sour cream and chives and little tiny bacon bits and pieces of toast! And then they’ll probably want a salad bar! Why, they’ll be lined up for miles! If President Ford wants to be remembered as a great president in his final days, he should do something about the price of coffee! Not steak! It’s outrageous! I can’t believe what that man is doing–
Jane Curtin [played by Jane Curtin]: — Miss Litella –
Emily Litella: — What? What?
Jane Curtin: [speaking slowly and clearly] … That’s not “steak.” President Ford wants to make Puerto Rico a state. Not a steak — a state.
Emily Litella: Ohhhhh. Well, I’m sorry. [squints and grins] Never mind.…
Saturday Night Live, “Weekend Edition” (Jan. 15, 1977)
Kevin Corcoran
Apr 28 2023 at 11:39am
Hey nobody.really,
I’ve tried this a few times to no avail, but I’m a sucker for lost causes, so I’ll try again – seriously, just refer to me as Kevin, please. Being referred to on a last-name basis was something I never much cared for during my time in the military, nor am I a fan of it now.
That aside, I have a few thoughts.
Your initial “broadly speaking” comment, in my opinion, suffers from being far too broad. Elections are indeed one alternative to “RESOLVING DISPUTES WITHOUT A CIVIL WAR,” as you say, but they are hardly the only or best alternative in many cases. Scholars like the Ostroms, or James Scott, or Pete Leeson, among many others, have documented wide varieties of cases of people successfully “resolving matters that exceed the capacities of individual negotiation” without the use of elections and also “WITHOUT A CIVIL WAR.” Another interesting thing that comes from studying the history of these cases is how often these mutually agreed upon collective solutions are pushed aside by the state, not because the people found themselves incapable of coordination a solution on their own and were therefore on the verge of “A CIVIL WAR,” but because the people holding state power decided that lesser people simply shouldn’t be allowed to solve their own problems in their own way. Your comment that “societies have adopted elections” as a means of solving these problems, aside from being historically suspect, makes the very mistake I was warning against – speaking of “societies” as though a “society” is an agent who make choices, in a way that is relevantly similar to the way individuals do.
Nonetheless, I’m happy to admit that there are indeed cases where democracy or elections can very well be the best (or least bad) alternative available. But nothing in your comment convinces me that in order to obtain those benefits, we have to pretend to believe things we know to be false. However, I do see a very real danger in overselling what democracy entails and pretending election results mean something they don’t and can’t mean, or carry a moral authority they don’t posses. The more democracy and elections are put on a special pedestal as embodying “the will of the people,” and the more of a magical aura this “will” is seen as embodying, the more people will be inclined to use this “will” in all areas of life – recall, for example, how philosophers like Michael Waltz have come to argue that “the will of the people” not only real but is also inherently just. When people come to believe both that “the will of the people” is both a real thing, and inherently just at that, they will naturally want this real, inherently just thing to be applied in all areas of life. And why wouldn’t they? To forbid something that is inherently just, after all, would be an injustice.
I agree that avoiding civil war is a good thing, and I agree that elections and a willingness to accept their results can be one way of doing so. But we should widen our gaze here. It seems to me that an even better way to avoid A CIVIL WAR would be to expand, rather than restrict, the ways in which coordination problems can be solved, and the more we oversell what elections mean and do, the more we needlessly restrict the scope of options available. I’m currently reading David Schmidtz’s new (and thus far excellent) book Living Together: Inventing Moral Science where he asks what I think is the right question: “How do some societies make it normal that people mind their own business and avoid getting in each other’s way? What enables most people to be amazingly adept at knowing what others will count as minding one’s own business?”
We don’t achieve that by overselling both the meaning and content of elections, or deciding to pretend election results mean more than they do. The more and more scope we grant to elections, the more impossible we make it for people to avoid getting in each other’s way. Everything becomes a contest about who really reflects “the will of the people” and is thus justified in imposing that “will” on everyone, in every area.
nobody.really
Apr 28 2023 at 6:09pm
1: Sorry about the name! I have a terrible memory for names, so I doubt that I will remember to refer to you by your first name. But perhaps I could remember to adopt the convention of simply using people’s entire web name rather than an abbreviation. I’ll try it, anyway.
2: Much of my comment reflect themes from Francis Fukuyama’s Liberalism and its Discontents (2022). Liberalism arose from the crucible of Europe’s endless religious wars, and whatever its shortcomings, it sure looks good by comparison. But perhaps we can better distinguish elections from other aspects of liberalism?
3: I look for ways to resolve collective issues. And I welcome learning about options that go beyond war and elections. Do you have some specific conflict resolution strategies in mind?
For example, we might identify … private property rights (“good fences make good neighbors”)! I argue that private property rights reflect a social convention for resolving conflicts, and thus people can seek to extend or restrict application of this strategy as changing circumstances make it more or less appropriate. (E.g., Does it make sense to develop a cap-and-trade system for regulating externalities, whereby people obtain property rights to pollute? In the absence of a mechanism for monitoring, tracking, trading, and retiring emission rights, this makes little sense. But with these innovations, maybe this makes better sense?)
Some libertarians may agree with me. Others may not, arguing that private property rights transcend the status of useful social convention and enter the realm of religious dogma. But the argument becomes iterative: A libertarian might concede weaknesses to the private property concept, yet still argue that the concept does more harm than good—and that the best way to defend the concept is to endow it with quasi-religious significance. And thus we return to the question of whether social cohesion requires the embrace of myth….
4: Problems with promoting deference to elections:
Sure, I use “societies” as a shorthand when I have no need to focus on a specific individual. Would it help if I used terms such as “collective” and “the state” instead?
Anyway, here I don’t know that you identify a problem with elections so much as an advantage of subsidiarity—attempting to resolve collective disputes at a level most proximate to those in conflict. Imagine that a collective decision gets pushed aside by someone who claims to rule by divine right rather than by winning an election. Does that make the situation better? If not, then I don’t see elections as the source of the problem.
Mostly I recommend using elections to resolve conflicts among equals, not between superiors and subordinates. As Thucydides remarked, “Right, as the world goes, is only in question between equals in power, while the strong do what they like and the weak suffer what they must.” We all endure bad decisions by superiors, whether or not the superiors achieve their status via elections. But elections provide a mechanism for removing elected superiors, which tends to make the superiors somewhat responsive to the electorate. That seems like an advantage to me.
If you want to argue that sometimes elected officials make bad choices, and thus we should maintain skepticism about elections—or indeed about any other method of conflict resolution not based on 100% consent of those affected (a la Buchanan?)—I will concede many of the points. Likewise I might concede that I cannot know anything beyond “I think therefore I am.” But I question the practical application of these insights.
I don’t know Michael Waltz’s views—nor Kenneth Waltz’s, for that matter. But I if this illustrates your concerns, I suspect that our views may not conflict.
I want to develop methods for resolving conflicts short of civil war—and to get people to embrace those methods. I surmise that you want to avoid oppression by the powerful. I think we could embrace a common message: We should recognize and affirm the outcomes of elections—and also embrace limits on official power, whether or not a given official achieves her status via election. The conceptual shortcomings of elections as a method of conflict resolution do not justify insurrection. And winning an election does not justify overreach. Within that framework, we can dispute the optimal methods for structuring and administering elections, and the appropriate limits on executive/state power.
This one is so new, it doesn’t appear on Schmidtz’s Wikipedia page—er, David Schmidtz’s Wikipedia page. So when you get done, give us a book review! I’m looking for my next Audible selection.
Kevin Corcoran
Apr 29 2023 at 10:46am
Just a quick reply here, since I don’t always have the time to write essay length comments. Time is a very scarce resource indeed with an almost three year old, an eight months old, and an overly hyper dog, all of whom require constant attending!
No, and for a specific reason. Attempting to identify, in advance, the “specific conflict resolution strategies” that people should be expected to use to solve collective issues makes one prone to committing what I have very clunkily called the 5-1 error. That is, when we decide in advance, from our armchair, that conflict resolution strategies will take such and such specified form, we can very easily fail to see the actual, varied, and unique forms of strategies people come up with, and wrongly conclude that a problem exists when none actually does. The variety of ways people can and have come up with to deal with these issues far exceeds what either you or I would just be able to imagine a priori. Property rights are of course just one way to deal with this, but the Ostroms in particular have examined all kinds of ways people have been able to solve collective action problems in the absence of secure property rights. But each “conflict resolution strategy” is a unique, organic, and evolved method particular to the issue and people at that time and place. Attempting to specify what those methods will be in advance is to put unnecessary intellectual blinders on, and leads to a sort of tunnel vision that makes one prone to overlooking those systems.
Those are indeed two possible ways one might think of private property rights. I don’t subscribe to either, however.
I’m actually working on a series of posts, in a similar spirit to my ten part series on Jeffrey Friedman’s Power Without Knowledge, reviewing another recently released book that examines and critiques this very claim, as it happens. It’s not the aforementioned book by David Schmidtz, which was only just released in the last week or so. I may or may not cover that book in the future, but I suspect its one you would enjoy. Schmidtz argues in it that the question “how should we live” is assumed to be foundational, but an even more foundational question is “how do we live together” – that is, what modes of living make for a safe, flourishing, prosperous, and healthy society is the first question to ask, and then within that framework we can begin to examine the question of how to live. But I’m not sure if I’ll do a write up on it yet – I’d have to finish it and digest it for a bit before I make that decision.
Richard W Fulmer
Apr 27 2023 at 11:34am
The fallacy of equivocation often crops up in political and philosophical debates. For example, in one of Socrates’ most famous dialogs, the philosopher disputed definitions of justice posed by various Athenians. The traditional Greek understanding was offered by Cephalus, who stated that justice is being honest and giving to each what is owed him. In response, Socrates posed a thought experiment. He asked Cephalus to imagine that he had borrowed weapons from a friend. When the time came to return the weapons, however, Cephalus’s friend had become violently insane. Socrates asked if it would be just to return the weapons, given that the madman would likely use them to harm or even kill innocent people. Cephalus admitted that it would not.
Socrates claimed to have shown that Cephalus’s definition of justice led to a basic contradiction, thereby proving it false. But Socrates did no such thing. Rather he performed a bit of verbal legerdemain by conflating two separate virtues: justice and prudence. By Cephalus’s definition, returning the madman’s weapons would be just. Cephalus owed the weapons to his friend and justice demands that they be returned. Returning them, however, would not be prudent. Socrates’ scenario pits the two virtues against each other, but a reasonable person could come to a compromise that kept people safe while still repaying the debt.
He who controls the language controls the debate.
David Henderson
Apr 29 2023 at 10:52am
Excellent post! And, as a bonus, I learned some new words.
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