Hotelling’s Law (2011)
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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....
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) =
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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.)
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.
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.
This assumes some features of the distribution of visitors that aren't specified in the problem description.
Aren't I correct, HN?
Satirize that, n-gate.com
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.