
Hotelling’s Law (2011) - tosh
https://www.uh.edu/engines/epi2692.htm
======
keyle
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).

~~~
coldtea
> _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.

------
noonespecial
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".

~~~
alangpierce
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.

~~~
mmt
> 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.

------
AnthonyMouse
> 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.

~~~
JumpCrisscross
The radicalisation in our system seems to result from the primary process, not
the general election.

~~~
ahartman00
There are a few reasons:

"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....](http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0123507)

------
lucas_membrane
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?

~~~
red_admiral
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.

In practice, base64(solution) =

RXZlcnlvbmUgcGlja3MgdW5pZm9ybWx5IGF0IHJhbmRvbT8gTXkgZmlyc
3QgdGhvdWdodCBpcyB0aGlzIG1pbmltaXplcyB0aGUgcmlzayBvZiBiZW
luZyAic2FuZHdpY2hlZCIgYnkgeW91ciB0d28gY29tcGV0aXRvcnMu

?

~~~
lucas_membrane
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.

------
dramm
... 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.

------
kazinator
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.

------
dang
Related from 2015:
[https://news.ycombinator.com/item?id=10787515](https://news.ycombinator.com/item?id=10787515)

------
quickthrower2
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.

~~~
cbsmith
Yeah, but for the same reasons, they'll be driven to offer nearly identical
pricing, flavours, etc.

------
candu
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.)

------
kokey
The application of it to politics is particularly noticeable in mature
democracies with a first past the post type system of elections.

~~~
dmurray
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.

~~~
syrrim
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.

------
lisper
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.

------
zappo2938
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.

------
MPSimmons
How did I make it through the entire article and this entire comments section
and not once see a link to a Nash Equilibrium?
[https://en.wikipedia.org/wiki/Nash_equilibrium](https://en.wikipedia.org/wiki/Nash_equilibrium)

------
multibit
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?

~~~
InitialLastName
The funny thing is that supporters of either party would read "the obvious
corruption of one of the parties" as referring to the other one.

------
ikeboy
>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.

------
jancsika
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.

Aren't I correct, HN?

Satirize that, n-gate.com

------
crdoconnor
>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.

~~~
itchyjunk
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?

~~~
jds375
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](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.

