The Paradox of Intransitive Preferences

[@HeavyMetalMouse]

One of the main issues with the intransitive preference actor is that his preferences are 'irrational' as per the model. Therefore the model cannot possibly predict what he will *do* with those preferences; it is the model that breaks, so it is not surprising the result is nonsensical. The question becomes how to incorporate those possibilities into a model that does behave well. One notable thing about your example is that the cyclic preference occurs because of an externality, rather than any sense of internal value of the choice. It is possible that, absent any externalities, the preference cycle would vanish, thus uncovering the person's 'understanding of value' - their willingness to part with money for an 'improved' option based on their overall preferences might not reasonably extend to violating this sense of the underlying 'understanding of value' of the things. On the other hand, the existence of a cycle like this might be evidence that those preferences are not strongly held - that the individual is falling victim to a known mental bias: "Strong Decision" Bias. When presented with two options, the brain does not want to be indecisive, it wants to make a decision about which it wants more, because not doing so leaves unresolved tension. 'Not knowing' or 'Not deciding' is, in many cultures, not an acceptable thing, even in situations where it is stated to be acceptable - they ironically prefer having a strong stated preference to having a weak stated preference. So while the subject may *express* cyclic preferences this way, one or more of those preferences are likely to actually be 'weak preferences', in that they are mostly indifferent, but would choose if they had to (which the presentation of a choice implies they have to). This means that, if they already have one choice in that 'weak preference', there is no actual pressure to 'upgrade'. The model also ignores the 'cost' associated with changing your choice. If you have one choice, but a choice you would otherwise strongly prefer comes along, you as a rational actor still might not change your choice, simply because the very act of changing your choice is, at minimum, a cognitive cost. Unless the new choice is more valuable to you 'enough' that you're willing to overcome at least that cost, it functionally doesn't matter that you prefer the other thing - you don't prefer the 'other thing plus the cost of changing selection' to 'having this thing'. This becomes more pronounced if we also include other possible costs that changing selection would have: in the example given, getting the Haunted House + Family option implies that they are able to arrange the event with family; once that option is obtained, the cost now includes the preferences of the Family, and how changing his choice will affect them, as well as affect him socially ("I made plans to go with you, but I decided I'd rather go alone" is very different from "I had a choice to plan to go with you, or plan to go alone, so I decided to go alone"). Overall, it seems like the existence of an expressed cycle of preferences within a single individual indicates that something the model has not considered is happening - whether that be hidden costs, or an error in extracting those preferences, or similar. Sadly, even when acting rationally, people do not always *communicate* rationally, which can make understanding their internal state extremely difficult, imprecise, or even impossible in cases. "Hell is other people."

[@stevehorne5536]

Why do the arrows point AWAY from preferred options? Intuitively, preferred options are things that people move towards.

[@fullfungo]

I think the notation is based on A -> B being A > B in terms of value.

[@samgordon9756]

A -> B is equal to “A to B” when the quote is spoken out loud. The graph/map is agnostic to what it is representing. It represents a preference for A -> B and going from A -> B.

[@stevehorne5536]

@@samgordon9756 That "A to B" is precisely why it sounds like B should be the preferred option to me - "to B" as in B being the option the person is inclined towards. Of course graphs are a general thing, I know that, but I still wouldn't draw a digraph representing routes leading to goal G with all the arrows pointing away from G.

[@WrathofMath]

It is to have congruency with the phrase "A is preferred to B". Similarly the arrows allow us to move from A to B. I agree it's a little odd, but I personally find the arrows going the other way more odd, because Id consistently be gesturing from the more preferred option to the least preferred, hence opposite the direction of the arrow.

[@qsquared8833]

I find this very counter intuitive as well

[@nathanisbored]

i would say the paradox comes from the fact that their preferences in this particular case were not static. at the beginning, they did indeed prefer hay ride over house, but by the time it came around again, given everything that happened, their preference has changed direction, or at least they are less willing to to choose something else because they are too committed now. but either way, it can be modeled as their preferences changing over time, so the arrows change direction after youve already started traveling the path

[@MichaelDarrow-tr1mn]

There are two choices for the haunted house. One is better than the hay ride and one is worse.

[@FaerieDragonZook]

I believe there was a Dr. Seuss book about this principle, or at least a very similar principle

[@HeavyMetalMouse]

Indeed, "The Sneetches" - a story with a surprising number of layers of applicability.

[@malvoliosf]

Someone who suffers from both an intransitive set of preferences AND the endowment effect cannot be exploited in this fashion. Yes, presented with A or B, perhaps he would choose B, but if he already has A in his possession, he wants to keep it.

[@stevehorne5536]

And while I don't know the term "endowment effect", it's well known in psychology that we humans have an "irrational" aversion to losing what we have, that prevents us gaining significantly better things in exchange. Of course how "irrational" that is is debatable given the possibility that what you're promised or otherwise expect to gain may not be achievable in reality, leading to expressions like "a bird in the hand is worth two in the bush". When experience - both cultural and evolutionary - reaches a different conclusion to theory, maybe the theory is flawed. And theory is actually almost always intentionally inherently flawed. It's called abstraction, and it allows theory to focus on a certain aspect of a problem and reach a conclusion based only on that aspect, when the actual real-world circumstances (1) are too complex to allow a conclusion to be reached, and (2) don't generalise to other circumstances to teach a useful lesson and be worth describing because they're too specific to one particular set of real-world circumstances that will most likely never recur. And in practice it's a very good idea to be informed by theory, even though we also need to be aware of the limitations due to the abstractions its based on. Not a criticism - after all we all still need to stay in practice seeing the limitations of abstractions, but I bet teachers have an intransitive preference cycle - they prefer students to learn, so they prefer students to be aware of the limits of abstractions, but they're also sick of hearing about them and prefer to remain sane, so there must be a way to construct an intransitive cycle out of that. Actually, another thought. You might expect traders to sell or exchange things based on the relative value to them. Trade usually depends on different people having different degrees of preference to the same things - relative to the buyer, the seller values the money a bit more than the product being sold. This model depends on the exploiter having a higher level awareness of the problem - that's exactly what this model of the problem expresses, a higher-level model of the problem than the person with the preferences is assumed to have. But it's interesting that this model assumes exploiters have higher level awareness but other people don't.

[@iwersonsch5131]

The endowment effect is not irrational as long as you model endowment as being an attribute inside the state that is being preferentially evaluated

[@danielrhouck]

It is definitely possible to get real-life humans to show non-transitive preferences. Now I might misremember, or I might be thinking of a bad study that does not replicate, but I think if you do this and start money pumping them, some will *notice* but keep making the trades, which seems strange to me. I can imagine having non-transitive preferences, and being money pumped about them for a cycle before I catch on. I can imagine a good con artist distracting me so I don’t catch on that quickly, and being money pumped further. But I can’t imagine being in that situation, noticing the money pump, and still giving away money without taking a minute to decide which option I actually want most and stopping there. But IIRC, some people do

[@colbyforfun8028]

Maybe the hassle of making an exchange is a negative that breaks the cycle in some way. You’re not choosing between 2 options, you’re choosing between an option you already picked and exchanging it for another, which may be different. Also the sucker may realize he is being suckered and either realize his preferences are irrational and change them, or refuse to do business out of pride.

[@yowza9638]

8:25 No, you're willing to give B away for A, but not give A away for B, so you clearly have a preference. You don't need extra money. Once you start giving a cycle, part of your cost analysis is not only what you're buying but the cost you spent to get to that iteration of the cycle.

[@Stellar_Lake_sys]

one way for intransitive preferences to work that comes to mind is that, from the state of having no item in the cycle, given the choice of any pair it seems to form a loop, but once in the cycle, not changing acts as an option preferred to any neutral or costly trade. the cycle only describes a potential state of indecision (probably avoided by a true equilibrium of biasing factors being almost nonexistent), not a willingness to change once already having made a choice once.

[@quan7umjack]

So do you choose bulbasaur, charmander, or squirtle?

[@Galinaceo0]

There's a few things i can imagine that prevent the pump. First making negotiations takes time and effort which might not compensate the value gained by each transaction. Even if that is not the case, the preferences can change every time a transaction happens, so after a few switches they might no longer have that cycle of preferences. Another possibility could be that maybe the value of each exchange is so small that no amount of money compensates for it. This could be modeled using a non-archimedean real closed field like hyperreal numbers maybe.

[@pion137]

I see only two ways to apply this in a real world scenario, keeping a rational actor. If you present them with a myriad of choices, where you present only binary options at each state, and then cycle the many choices with pseudorandom repetition. As in you have a list of say 100 items you can pick. I present you with only 2 at a time and you choose your preferred item. You can keep it or move on to the next round. Each time you move on, you get a new binary choice where the items are novel relative to each other with some quality, like color or functional vs aesthetic. No pair is repeated, but items you've selected then moved on from would be re-presented in a later binary scenario, but the frequency of the reappearance would be weighted to appear slightly more often than the items you didn't choose, which would have a complimentary weighting. It would easily obfuscate a rational actor's ability to quit playing and paying. A second way is to programmatically force a proxied rational actor to go broke Say you gave a person an automata that has a preset list of the person's preferences. Essentially, giving the person a list to spell out their preferences in a binary way as with the scenario above, but with perhaps a smaller list such that every combination of preferences could be hashed in the list. This would be more geared toward auto-trading or something. You could then have your code always present a "better" option, where even if there's a sound transitivity chain, so long as you know both sides, you could have your "presenter" automata trick the "chooser" automata in binary choice. Obviously, to avoid suspicion, you'd have to temper the number of automated exploitations for the perceived value of return expected by the person. If they use the bot to decide and try to get the best outcome, you'd feed it modestly better choices or similarly, worse choices, each time charging a small amount extra for the ability to make another choice. once you've done this such that they are now paying moderately more for some ultimately preferable item than they'd pay otherwise, you can present them with their top choice and at this point, their "chooser" bot would stop and the transaction would complete. For this to work it would have to be something of volatile value, such as stocks, as if the things being chosen have some locus of intrinsic value, like stuffed animals at a carnival, there would be a perception of being ripped off by the person and then other people wouldn't want to participate.

[@stevehorne5536]

Another option is the exploitee isn't a particular person (or automaton), but people in general from some population. Even assuming that they all have identical preferences, they're probably not aware of all the other exchanges that are occurring. This situation could arise in practice in distributed computer systems - there's a certain latency before one computer becomes aware of what's happening at another. That's not just about detecting exploits, it could also give rise to those violations of transitivity as limits of current local knowledge may prevent one computer in a system from perceiving value precisely how the overall system is intended to. Or for a human example, different bookies may offer exploitably different odds for bets on the same event.

[@jbrecken]

The money pump changes the situation, though. It's no longer "Do you prefer A to B?" but "Do you prefer A and less of your money to B and all of your money?"

[@NStripleseven]

That’s the thing, though. The overall outcome is like that, but each individual exchange was something Mr. Ic would prefer to make than not to make. Obviously the outcome is ridiculous, but the fact that we have arrived there by an entirely logical line of reasoning must mean that we have made some invalid assumptions (eg. that our preferences/degrees of preferences were universal and unchanged across different scenarios)

[@authenticallysuperficial9874]

It doesn't matter. If you prefer A to B then there exists some action you would take to move from B to A, and thus some amount of sufficiently divisible money you would be willing to fork over.

[@dragonfractal6361]

How is Mr. Ic more concerned about looking like a coward going to the haunted house with family than he is about looking like a fool by exchanging his tickets multiple times with the same person? Mr. Pump should at least have two assistants on his team to help him out.

[@WrathofMath]

That's a good idea! 🤣

[@qsquared8833]

Its possible to induce intrasitivity at least temporarily through forcing combinations of options and/or changing availability of options over time. Its also valid for preferences to change due to external factors. In your example, of mr ick, its external factors which cause rhe preferences ro flip IMHO. If you also consider things may have sepeeate factors which have rheir own transitive preferences, such as how kuch money you can spend, outcomes which are likely, and experiances to be had, as well as social pressures, you can find people prefering a sub-optimal preference that in a vaccume would be further down the chain of preferences. You can still view all of rhese rhings as being transitive preferences ao long as tou add more dimensions, but in simple views of abstracted valuation it would look like transitiveity is broken. Basically youc an force peoples preference or all they can choose to be rhe option you prefer by playing with other factors outside of their natural preferences. We see thisnall the time in the real world economy where corporations exploit their customers by creating packages to force them to spend more money, ot choose less popular options to maximize their net revenue

[@ethos8863]

You could argue it's still a preference even with no compensation because they would do an exact exchange in one direction but not the other

[@JynxSp0ck]

Intransitive preference exploitation also takes place on a national level but we tend to call those "elections".

[@plushloler]

I don't think anyone can actually have intransitive preferences in real life. If I ask Mr. Ic which of the tickets he would like, would he even be able to pick? Would he say that he is indifferent? It just makes no sense to have intransitive preferences, I think it would only happen by accident and in a manner where you would not notice it, because as soon as you did, you would start figuring out a transitive system instead.

[@authenticallysuperficial9874]

Yeah it really does not sound like he set up a system of preferences which can in fact obtain. I'm not saying there isn't one, but none plausible was presented in this video.

[@Gamesaucer]

There's nothing to suggest that people can't have intransitive preferences; the problem is that this model's representation of intransitive preferences it itself nonsensical. For example, take rock-paper-scissors. I have a preference for paper over rock, simply because paper beats rock. For the same reason, I have a preference for rock over scissors, and a preference for scissors over paper. Of course these are _actions_ rather than _possessions,_ but the same thing is true for intransitive dice. Of any pair of dice, I'd rather have the die that beats the other one. However, if I'm offered the choice between all dice all at once, I'll just pick the one that rolls highest. Still, if you'd then offer to freely trade me for the die that beats that one, I'd probably take it. This shouldn't be counterintuitive. The issue is that you can't model this kind of system by just assigning each option a set value. The value depends on the options on offer. Furthermore, it depends on external factors. I might stop trading dice altogether after a few goes just because I have a preference against trading forever, and that preference has grown strong enough to overrule my intransitive preferences. And of course, just because I have a preference in practice (i.e. I'd take A over B if given a free choice) that doesn't mean I'd be willing to give money to switch from B to A. My preference might be of a kind that I am unwilling to attach a monetary value to, either because it's so comparatively weak (in which case any amount of money at all will dominate a trade) or because it's so comparatively strong (in which case no amount of money will ever dominate a trade).

[@elmaruchiha6641]

I think it is possible to have that cycle. It could be that someone whould prefer A to B,such that this someone whould like to change B with A and pay in total of all trades to get A 2€ for axample.

[@ilikechess-22]

Neat view even though I haven’t watched it yet

[@lukeburris1011]

In order to set up the scenario of Mr. Ic, you're relying on a mindset of 2 choices to fit a 3-choice system. In reality, Mr. Pump would offer the ticket trades, and Mr. Ic would recalculate his preferences based on the knowledge he has about his 3 options, and resolve the intransitive problem because now he has no reason to fear being seen as cowardly if he goes on the hay ride. Alternatively, he still has the fear and you've lied to us about his preferences earlier.

[@saeedgnu]

None of this is very relevant to real world. Because we need to "think" at least a little to figure out our preference. But our preference also depends on our emotions and mental state, which are *constantly* changing. We are of course prone to psycological influence and trickery, but that does not conform to any Math. Real world is much more complicated and messy.

[@ric8248]

l don't think it works, unless the intrasitivity was very complicated and the preferences were very close to indifferent between options. ln this case the preference "haunted house with family" over "haunted hay ride" looks very dubious considering the arguments.

[@HopUpOutDaBed]

people don't have infinite wealth though. In a real life scenario, someone might have budgeted $20 for a fun night out, and after a couple cycles of money pumping (assuming they didn't even realize they were being swindled in the first place) would run out of their budget and would decide to just stick with their choice rather than spend more. From an economic standpoint this is explained by the diminishing utility of money - having less money means they value the money more than the difference in preferences.. In practice I think a larger chain of money pump could work, but would reach a choke point where the value of the dollar of the spender becomes worth more than the time/effort of exploiting them, and thus the chain breaks naturally.

[@Gamesaucer]

imo a rational actor should be able to see that after traveling the cycle once and trading away a bit of value each time to satisfy their preferences, they'd end up in the same spot again but with all that value they traded away lost. So it's a strictly worse situation than the one they're already in. This means even if they've agreed to all but the final transaction in the cycle, they must consider the value lost to get there in order to get back to where they were, which is strictly not worth it. As a result I'm only semi-vulnerable to the money pump. But I have another objection that is much more fundamental, and whose effects can actually be observed in reality. The gist of it is this: people, in general, have a preference for keeping what they already have, and consequently a preference _against_ trading away what they have. For instance, if I had a friend who wanted to swap drinks with me, I might decline, even if I have no preference for either drink and I _do_ have a preference for my friend's happiness. The reason might be that I don't want to give away _my_ drink... simply because it is _mine_ and for no other reason. But where this becomes a more fundamental issue is in the fact that the very state of having something (or even just anticipating something) and the very act of trading something both change the equation. This means you can't travel a preference cycle without changing the nature of the preferences of the person you're trading with. Therefore, there are two important assumptions here that do not hold: - The assumption that trading A for B and subsequently trading B for C is the same thing as trading A for B and B for C in isolation. - The assumption that having a preference for B over A means that you'll therefore trade _your_ A for a B for the difference in value. And perhaps most important from a theoretical standpoint, the very existence of an intransitive cycle in preferences means that preference cannot merely be modeled as a number, because numbers _are_ transitive. If you try, you create a singularity where A must be greater than itself, which can by definition never be true, and therefore an intransitive preference cycle as modeled in the rational choice model is also by definition unsound.

[@jasonremy1627]

Your model presumes that all value is equivalent to dollars. There are multiple kinds of value which are non-fungible. Which is to say there's some kinds of value which cannot be exchanged for money, but which still motivate human behavior. And which are still rational. The equating of money with other forms of value is a rather weak axiom to impose in your model, and ultimately makes it not very useful.

[@mushykitten]

very uninteresting video. sets with an intransitive complete ordering on them can have cycles in them. what a basic fact that doesn't deserve 10 minutes of a video...