That's because FPTP encourages a two-party system. If you add a third ice cream vendor, Hotelling's law breaks down and there is no stable equilibrium.
The third party can fill a very useful niche: when your current party has let you down, but you also don't want to support the other extreme of the political spectrum, you can vote third party.
This has no analogy in hotellings law proper. But imagine the beach had two entrances: one at 1/4 down the beach, and one 3/4 down the beach; there are more beach goers near an entrance than farther away from it. We also recognize that a beach goer is less likely to get ice cream the farther away from the ice cream stand they are. Then we will see something similar as before, with the vendors moving closer and closer together. But now they stop before they reach the center, because if they get to far from the entrance they will start losing customers. This explains why political candidates are not precisely identical, just similar: they are each catering to a block of more extreme voter.
Now we add a third entrance somewhere in between the first two: what happens? We would expect three vendors to emerge, one for each entrance, all with a tendency towards their second closest entrance. This is analogous to three political parties, with two being more similar to each other than the third, as we sometimes see outside the US.
In short: the political parties in the US are particular to the politics and distribution of the voters there, and efforts to paint this as inevitable given FPTP are severely overstated.
>One of the most commonly pointed to examples of Hotelling’s Law arises in politics. When candidates position themselves too far left or right, they can lose the vote of centrists.
Parties becoming mirror images of one another can be equally well explained by both candidates being bought by the same groups.
But that hypothesis fails to apply to ice cream vendors case. If the hypothesis from Hotelling's Law already presents an explanation, why come up with a special hypothesis to describe this scenario?
Just because a rule applies to more cases doesn’t mean it’s the best answer for a given case (or that we should prefer it over other rules). Consider this example that’s true for many cases, but overall not a sufficient proof https://en.m.wikipedia.org/wiki/Pólya_conjecture
In fact, I’d be willing to bet both hypotheses contribute to the overall effect we observe.
I guess it's worth asking, if it weren't for a few key religious issues and the obvious corruption of one of the parties, how differently would they stand ideologically?
>It’s not hard to see that unless the two carts are situated side by side in the middle of the beach, there’s economic incentive for one or the other to move.
This assumes some features of the distribution of visitors that aren't specified in the problem description.
Isn't competition at the end of the day a bit of a discussion? Parties are fighting towards a certain goal and there is always a middle ground: "we're all trying to make great fridges". And through a history of working out what works and what doesn't, you end up with roughly the same solution (to the joy of the patent lawyers).
>and there is always a middle ground: "we're all trying to make great fridges"
Not really. They're all trying to capture the market and increase their profit as much as they can.
Once a company reaches a certain size and it's not about some individual's personality and dreams of building products anymore, if it could -without repercussions- sell heroin to children, they'd jump at the chance. Most will settle with less evilness, like polluting the environment, selling things they know it's half-hearted made crap, using sweatshop labor, and so on.
This always seemed to fall down for me in that some people who were willing to walk 1/4 mile for ice cream won't be willing to walk 1/2 mile. You have to make huge assumptions to call this any sort of "law".
I would imagine in the fridge example that results in a product category. In the ice cream example, the carts would move as far possible towards the middle until the incentive is no longer an incentive. They're already in the middle, or going any closer would lose rather than gain customers. But afaict the general idea still holds, theres an inherent incentive to move to the middle (which ofc can be defeated by competing incentives but nonetheless)
This is a great point even outside the metaphor -- voters will stay at home if neither candidate "speaks to them", and if the voter distribution is "lumpy", a third candidate angling to own the second-biggest "lump" can beat the two mainstream candidates fighting over the mainstream audience.
Assuming those preferences are normally distributed across the beach, both vendors will evenly split the opportunity cost, on average.
It’s certainly a reductionist metaphor, but it does seem to take this consideration into account. In fact, it’s kind of the point. The vendors split the opportunity cost, so they are at an equilibrium, but the beachgoers are not.
I'd say it's a significant result because it's a situation where natural competition causes a negative outcome for everyone. Having to walk 1/2 mile for ice cream is certainly at least as bad of an experience as having to walk 1/4 mile, probably strictly worse for most people. It seems likely that both vendors will lose some customers compared with the original scenario, and that the average customer experience will be worse.
If the same person ran both carts, or if they were run by the government, then they would be spaced far apart (the original position), which would be better for everyone.
I agree that the spacing would be, overall, better, but that, by no means, guarantees that the monopoly would be better. We have plenty of historical evidence to the contrary.
It's important to keep this particular economic "law" in perspective: it's a very specific, negative effect of competition. It doesn't mean that competition on the whole is undesirable.
> When candidates position themselves too far left or right, they can lose the vote of centrists. So there’s a natural pull toward the middle of the political spectrum.
This obviously doesn't work for first past the post. The two candidates with the most similar platforms will split the vote and lose to a third candidate with a different platform. The only way to prevent this is for the two candidates to each be far enough from the center that a more extreme third candidate would split more of the vote with one of the existing candidates than they would each have to split with each other, ensuring that the third candidate would not win and thereby deterring them from entering the race.
This doesn't work. If a third candidate comes along and places themself anywhere along the beach that the two candidates are in the middle of, they'll lose to the candidate opposite. (I think the single-dimensional political axis is also just a simplification, and the theorem works in higher dimensions.)
For a distribution of voters without statistic lumpiness or cross-correlation, I think the only way for a third candidate to win is to identify some neglected political axis. (Maybe the theorem holds if the voter population is convex?)
I think the point you are trying to make is that voters don't just always choose the politician exactly closest to them -- they pick one with some likelihood based on its relative closeness. In that case the two identical centrist candidates will split the vote.
Other circumstances the theorem has difficulty with are primary votes. If only left-leaning voters vote in left-party primaries, "centrist for lefty-party" candidates will win lefty-party primaries -- not "centrist for the electorate" candidates. The theorem only really holds for "strong parties" that can choose their candidates and their positions, not the weird US free-for-all where essentially every candidate is an independent.
I don't think that's a good analysis or refutation of what actually happens. What actually happens is the formation of political parties: All the candidates on the "left" would prefer that anyone on the "left" wins over someone on the right, so they merge into a single candidate in order to ensure they have the winner. The other "side" does the same. But then, given that there's only one candidate for each side, they get pulled toward the center as describe.
"Partisanship has been attributed to a number of causes, including the stratifying wealth distribution of Americans [2]; boundary redistricting [3]; activist activity at primary elections [4]; changes in Congressional procedural rules [5]; political realignment in the American South [6]; the shift from electing moderate members to electing partisan members [7] movement by existing members towards ideological poles [8]; and an increasing political, pervasive media [9]."
This paper also attempted to quantify the polarization:
"We define a network of over 5 million pairs of representatives, and compare the mutual agreement rates on legislative decisions between two distinct types of pairs: those from the same party and those formed of members from different parties. We find that despite short-term fluctuations, partisanship or non-cooperation in the U.S. Congress has been increasing exponentially for over 60 years with no sign of abating or reversing. Yet, a group of representatives continue to cooperate across party lines despite growing partisanship."
... until one of the owners decides to push a cart up and down the beach bringing the icecream to the consumer, and the other copies that, and then one pivots to offer ice drinks, and one offers gluten free vegan icecream, but they go out of business because, hey it's Houston not California. And then the surviving vendor is put out of business by a robotic beach delivery service.
This explains not only lack of product differentiation among competitors, but the actual fact of there being "strips" for certain products. Strips of furniture places, bridal strips and so on. What are those ice cream vendors doing: starting the nucleus of some kind of food court in the middle of the beach.
It is interesting to think about what happens when a third vendor enters the market. This person will not be incentivized to located at the center of the beach. Instead, they will want to be a little bit to one side so they will get most of the business form one side of the beach, leaving the other two to split the customers on the other side. I've not worked out what happens after that, but it feels like it would be complicated.
On the other hand, there's a simple symmetry argument that no matter what happens, once you reach steady state (if you reach steady state) everyone has to be in the same location because everyone is reasoning the same way. To end up in different locations something has to break the symmetry.
When the two ice cream stands are next to each other, then the bathers will no longer select based on distance, but on other features. You might find them selling different ice cream, changing their prices etc.
So the the city just invests a little in some shaded ice-cream cart infrastructure at the quarter mile markers, providing the convenience for beach-goers the free market would not have been able to provide.
Throughout the 90s several fine dining restaurants failed in Las Vegas. What changed Vegas was in 98' opening the Bellagio with 13 fine dining restaurants all in the same building. Now it became a destination. From the point of view of a restaurant owner, it is very, very when another restaurant opens in the same area. There has to be a critical mass for them succeed because each restaurant brings customers for the others. Cities discovered this when creating entertainment districts. It might be many venders close together like the restaurants at the Bellegio are the draw.
There are variations of the problem that explore the benefits to/of competition when there are more vendors.
If there are 3 vendors and the vendors are allowed to collaborate, a coalition of 2 vendors will form, they will
place there stands at positions 1/4 and 3/4, same as the optimum for consumers with 2 vendors, and the 2-vendor team will get 3/4 the business, which they may share equally by side payments, and the outcast vendor will get only 1/4 of the business, regardless of where he locates. If he locates anywhere other than right next to one of the duopolists, however, the closest duopolist can then relocate closer to the outcast to decrease the outcast's market share. Thus, an unregulated market of 3 vendors with anticompetitive behavior allowed, will only match the optimum (for customers) that is attainable with 2 vendors and centralized planning. The labor and capital of the 3rd vendor produce no benefit to the customers. If you think that this situation is unrealistic, compare it to the market in the USA for steel back when a single firm with its center of production in Pittsburgh was dominant: the dominant pricing model for all firms was 'Pittsburgh plus.' This means that steel customers, regardless of which vendor they chose or where that vendor actually produced the steel, paid shipping charges from Pittsburgh. The customers got no benefit from the geographic diversity of the industry.
If there are 3 vendors, and if the beach is regulated so that each vendor must select his/her own location before finding out what locations the others have chosen, with collaboration and moving of locations prohibited, what locations will the 3 vendors choose?
If all three vendors know that the others are trustworthy, intelligent and learned in game theory, you might end up with the "everyone cooperates" solution that's optimal for everyone (1/6, 3/6 and 5/6 along the beach) especially if everyone knows the order in which the three are going to have to commit to their preferences.
My analysis long ago was that for this case, the equilibrium mixed strategy with three players was a random choice with uniform probability everywhere within the interval from 1/4 to 3/4 and no probability in the segments at each end. This means that for the people at the ends of the beach, the competitive solution with 3 vendors is not as good as the centrally planned solution with 2 vendors, but for those in the middle of the beach it is very likely to be much better. This lines up with the conclusion for the 2 vendor case that Hotelling found: competition with few vendors for somewhat differentiated products will favor consumers with average preferences.
It's interesting to consider what happens to the sunbathers!
In the article, sunbathers are treated as a passive, uniformly distributed part of this game-theoretic setup. If the sunbathers are active participants, however, the game changes. Once the vendors move to the center, sunbathers will too (except for those that value privacy, quiet, etc. more than ice cream (!?)).
Suppose that this "tourist clustering" effect has taken hold, and now some new vendors set up shop. They have very little incentive to set up anywhere except the middle. Gradually, you get a cluster of largely indistinguishable ice cream vendors, all vying for the custom of a large group of tourists...
...and you've effectively arrived at a beachside ice cream market where advertising is essential for success. (You've also potentially created a market to sell a more "authentic" ice cream experience to sunbathers who would prefer to avoid the tourist cluster at all costs, so that as the ice cream vendors in the middle consolidate another vendor can come along and set themselves up as the "alternative" choice.)
42 comments
[ 3.1 ms ] story [ 88.2 ms ] threadThis has no analogy in hotellings law proper. But imagine the beach had two entrances: one at 1/4 down the beach, and one 3/4 down the beach; there are more beach goers near an entrance than farther away from it. We also recognize that a beach goer is less likely to get ice cream the farther away from the ice cream stand they are. Then we will see something similar as before, with the vendors moving closer and closer together. But now they stop before they reach the center, because if they get to far from the entrance they will start losing customers. This explains why political candidates are not precisely identical, just similar: they are each catering to a block of more extreme voter.
Now we add a third entrance somewhere in between the first two: what happens? We would expect three vendors to emerge, one for each entrance, all with a tendency towards their second closest entrance. This is analogous to three political parties, with two being more similar to each other than the third, as we sometimes see outside the US.
In short: the political parties in the US are particular to the politics and distribution of the voters there, and efforts to paint this as inevitable given FPTP are severely overstated.
Parties becoming mirror images of one another can be equally well explained by both candidates being bought by the same groups.
In fact, I’d be willing to bet both hypotheses contribute to the overall effect we observe.
This assumes some features of the distribution of visitors that aren't specified in the problem description.
Not really. They're all trying to capture the market and increase their profit as much as they can.
Once a company reaches a certain size and it's not about some individual's personality and dreams of building products anymore, if it could -without repercussions- sell heroin to children, they'd jump at the chance. Most will settle with less evilness, like polluting the environment, selling things they know it's half-hearted made crap, using sweatshop labor, and so on.
It’s certainly a reductionist metaphor, but it does seem to take this consideration into account. In fact, it’s kind of the point. The vendors split the opportunity cost, so they are at an equilibrium, but the beachgoers are not.
If the same person ran both carts, or if they were run by the government, then they would be spaced far apart (the original position), which would be better for everyone.
I agree that the spacing would be, overall, better, but that, by no means, guarantees that the monopoly would be better. We have plenty of historical evidence to the contrary.
It's important to keep this particular economic "law" in perspective: it's a very specific, negative effect of competition. It doesn't mean that competition on the whole is undesirable.
Not everyone. It's a sweet deal for people in the middle.
This obviously doesn't work for first past the post. The two candidates with the most similar platforms will split the vote and lose to a third candidate with a different platform. The only way to prevent this is for the two candidates to each be far enough from the center that a more extreme third candidate would split more of the vote with one of the existing candidates than they would each have to split with each other, ensuring that the third candidate would not win and thereby deterring them from entering the race.
For a distribution of voters without statistic lumpiness or cross-correlation, I think the only way for a third candidate to win is to identify some neglected political axis. (Maybe the theorem holds if the voter population is convex?)
I think the point you are trying to make is that voters don't just always choose the politician exactly closest to them -- they pick one with some likelihood based on its relative closeness. In that case the two identical centrist candidates will split the vote.
Other circumstances the theorem has difficulty with are primary votes. If only left-leaning voters vote in left-party primaries, "centrist for lefty-party" candidates will win lefty-party primaries -- not "centrist for the electorate" candidates. The theorem only really holds for "strong parties" that can choose their candidates and their positions, not the weird US free-for-all where essentially every candidate is an independent.
"Partisanship has been attributed to a number of causes, including the stratifying wealth distribution of Americans [2]; boundary redistricting [3]; activist activity at primary elections [4]; changes in Congressional procedural rules [5]; political realignment in the American South [6]; the shift from electing moderate members to electing partisan members [7] movement by existing members towards ideological poles [8]; and an increasing political, pervasive media [9]."
This paper also attempted to quantify the polarization:
"We define a network of over 5 million pairs of representatives, and compare the mutual agreement rates on legislative decisions between two distinct types of pairs: those from the same party and those formed of members from different parties. We find that despite short-term fluctuations, partisanship or non-cooperation in the U.S. Congress has been increasing exponentially for over 60 years with no sign of abating or reversing. Yet, a group of representatives continue to cooperate across party lines despite growing partisanship."
http://journals.plos.org/plosone/article?id=10.1371/journal....
On the other hand, there's a simple symmetry argument that no matter what happens, once you reach steady state (if you reach steady state) everyone has to be in the same location because everyone is reasoning the same way. To end up in different locations something has to break the symmetry.
Aren't I correct, HN?
Satirize that, n-gate.com
If there are 3 vendors and the vendors are allowed to collaborate, a coalition of 2 vendors will form, they will place there stands at positions 1/4 and 3/4, same as the optimum for consumers with 2 vendors, and the 2-vendor team will get 3/4 the business, which they may share equally by side payments, and the outcast vendor will get only 1/4 of the business, regardless of where he locates. If he locates anywhere other than right next to one of the duopolists, however, the closest duopolist can then relocate closer to the outcast to decrease the outcast's market share. Thus, an unregulated market of 3 vendors with anticompetitive behavior allowed, will only match the optimum (for customers) that is attainable with 2 vendors and centralized planning. The labor and capital of the 3rd vendor produce no benefit to the customers. If you think that this situation is unrealistic, compare it to the market in the USA for steel back when a single firm with its center of production in Pittsburgh was dominant: the dominant pricing model for all firms was 'Pittsburgh plus.' This means that steel customers, regardless of which vendor they chose or where that vendor actually produced the steel, paid shipping charges from Pittsburgh. The customers got no benefit from the geographic diversity of the industry.
If there are 3 vendors, and if the beach is regulated so that each vendor must select his/her own location before finding out what locations the others have chosen, with collaboration and moving of locations prohibited, what locations will the 3 vendors choose?
In practice, base64(solution) =
RXZlcnlvbmUgcGlja3MgdW5pZm9ybWx5IGF0IHJhbmRvbT8gTXkgZmlyc 3QgdGhvdWdodCBpcyB0aGlzIG1pbmltaXplcyB0aGUgcmlzayBvZiBiZW luZyAic2FuZHdpY2hlZCIgYnkgeW91ciB0d28gY29tcGV0aXRvcnMu
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In the article, sunbathers are treated as a passive, uniformly distributed part of this game-theoretic setup. If the sunbathers are active participants, however, the game changes. Once the vendors move to the center, sunbathers will too (except for those that value privacy, quiet, etc. more than ice cream (!?)).
Suppose that this "tourist clustering" effect has taken hold, and now some new vendors set up shop. They have very little incentive to set up anywhere except the middle. Gradually, you get a cluster of largely indistinguishable ice cream vendors, all vying for the custom of a large group of tourists...
...and you've effectively arrived at a beachside ice cream market where advertising is essential for success. (You've also potentially created a market to sell a more "authentic" ice cream experience to sunbathers who would prefer to avoid the tourist cluster at all costs, so that as the ice cream vendors in the middle consolidate another vendor can come along and set themselves up as the "alternative" choice.)