Risk Tolerance

So i wrote a paper in one of my classes this semester
and my professor objected to my use of the phrase
"irrational level of risk tolerance", claiming that no
level of risk tolerance was irrational. i wish to
challenge this assertion from a market-based
perspective. Suppose i offer you a ticket which pays
$100 with 50% probability. Depending on how risk
averse you are, it would be rational for you to offer
to pay anywhere between $0 and $50 for the ticket. In
fact, if you were particularly risk-loving (or
desperate), it could be rational for you to pay some
price above $50 for the ticket. In a vacuum, there is
no theoretical maximum for how much you can rationally
be willing to pay for the ticket, as long as you pay
less than $100 – we can see immediately that paying
more than $100 for the ticket is irrational, although
this irrationality may attach to something other than
your measure of risk aversion. i claim, however, that
there is a market-based limit to how much risk
tolerance is rational. In particular, i claim that it
irrational to pay more for this ticket than the market
price..

What then is the market price for the ticket? Well,
there are any number of roulette tables in operation
in this country at any given time, and roulette is a
particularly easy game in which to hedge one’s bet.
Assuming no intangible benefit is derived from buying
the ticket beyond what is achieved by playing
roulette, and assuming also no transaction costs and
that one can split one’s chips as finely as one likes
on the roulette table, it is in fact irrational to pay
eg. $60 for the 50-50 ticket when appropriate
placement of chips on the table will yield a 50-50
shot at $100 for only $52.78 (putting 100/36 chips on
each of any choice of 19 numbers on a 38-number wheel
will yield exactly a 50% chance of winning $100).
Because there is such a large number of firms
essentially selling this 50% chance at $52.78, no
rational consumer will pay more than $52.78 for a 50%
chance of winning $100, regardless of his level of
risk tolerance..

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Gun Control

So i saw a lady knitting on my flight from San Jose to Chicago last weekend and, as a result, i finally understand the logic behind the gun lobby's arguments against gun control. Stick with me here..

Why does the TSA restrict what items may be brought onto airplanes? Presumably this is to keep us safe with respect to the other passengers on the plane. If we take an ultra-pessimistic view, we can consider everything brought onto a plane as a potential weapon and every passenger as a potential enemy. As such, in order to maintain my safety i need to be certain the rules applicable to the situation ensure that i can bring weaponry sufficient to prevent the other passengers from obtaining a substantial weapons advantage against me. This condition is obviously satisfied if there are no restrictions on what can be brought onto the plane, as it is then my own fault if i fail to bring an arsenal sufficient to overcome that of any other passengers. Another way to maintain my safety of course is for the government to put an absolute cap on the level of weaponry that can be brought on board. Then everyone runs up against this threshold and no one has an advantage..

This is where the knitting lady comes in. As far as i know, knitting needles are not permitted on planes; if that is true, the current system fails because the detection mechanism is not perfect as evidenced by the fact that the needles showed up on the plane. If knitting needles are in fact allowed, the system fails because it is not sufficiently clear what items may be brought onto a plane; knitting needles are far more dangerous than some other items that are not allowed, and nowhere is there a comprehensive list that can be universally applied. i know from personal experience that both of these failures materialize. i have brought four-inch knife blades and cigarette lighters onto planes numerous times since the regulations prohibiting those items went into effect; and i came perilously close to getting arrested once for daring to demand that the TSA make it clear to me what regulation prevented me from bringing alcohol onto a plane (i subsequently reported the offending officer and was assured by his supervisor that there is in fact no such regulation)..

If the government can neither make it clear what items may be brought onto planes nor effectively enforce the regulations it does promulgate, i as a passenger can have no assurance that someone will not bring onto the plane a weapon so much more dangerous than what i can bring that it jeopardizes my safety. Thus according to this analysis, in order to guarantee my safety on planes the government must either devise a system that establishes a strict limit on the acceptable danger level of weaponry brought onto the plane and find a way to ensure that this cap is enforced, or it must allow all weaponry to be brought onto the plane..

Of course this all needs to be balanced against such concerns as the danger armed conflict on a plane may present to those on the ground, and the capacity of overhead bins to contain massive arsenals, but at least i can begin to see the logic behind the gun lobby's insistence on loosening the gun control laws on the ground. The analogy to the airplane example is clear, and given the inevitable arms race that will play out between people trying to ensure their own safety and criminals intent on violating that safety, the last thing we need is a government-imposed system of unclear directives and sporadic enforcement that may deprive peaceful citizens of the means to protect themselves. The enforcement issue even becomes more relevant on the ground, where citizens do not have the luxury of knowing everyone around them has undergone a thorough screening..

The only hope for the other side in terms of a defensible position is to devise a system with laws that are perfectly clear and perfectly enforceable. In the absence of this, it will be difficult for gun control proponents to convince those who agree with the other side's logic..

In Defense of Google

So i'll admit that when i first heard of Google's recent concession to the Chinese government, i thought Google had finally become evil. Just goes to show you how much faith one can put in the Palo Alto Daily News. (You will notice that i am not including any direct quotes from the Palo Alto Daily News here, but that is only becuase i cannot find any way to access the paper online.) When i read that Google was censoring search results available to Chinese users, i assumed it would work like this: The Chinese government would supply Google with a list of Chinese IP addresses, Google would filter every request coming into its US-based servers, and Google would return a restricted set of results if the IP address matched the Chinese list. In fact, i can think of no other effective mechanism to censor the search results available to Chinese users. And if Google used this mechanism, that would indeed be evil..

Thanks to this week's issue of The Economist and an NPR broadcast last week, i've learned a little more about the arrangement though. Google is not blocking its US-based servers at all. What is happening instead is that Google is setting up servers in China itself, and my understanding is that as a condition of this arrangement Google is required to adhere to certain guidelines. According to several articles i've read, this has been standard Google practice in France and Germany for quite some time now. These local servers are put in place to augment the US servers and speed up certain searches, and to my knowledge there is no effort being made by Google or the Chinese government to block access to Google's servers in the US. So ultimately Chinese access to Google is not restricted at all; on the contrary, it is enhanced..

Not only is there a net advantage to Google's placement of servers in China, there is no loss anywhere in the process. Many searches (the non-controversial ones) are sped up, while the banned searches that must go through US servers are NO SLOWER than they were before. Of course, one possible disadvantage to this arrangement is the risk that someone doing a questionable search would stop at the Chinese servers, thinking the censored results were complete. However, Google has taken care of this problem by alerting Chinese users whenever search results have been censored. Once such a notice comes on the screen, the Chinese user can search on Google's US-based servers for the information that was censored..

The only efficiency problem this poses is a waste of time for the individual who goes to the Chinese server first only to find out she must subsequently search on the US server. Okay, let's run some numbers on this. Assuming that the time required for a search is independent of the topic of the search, there is going to be some threshold percentage of censored searches for a user beyond which it is more efficient to use the US servers for all searches. Let's assume that the Chinese servers are x times as fast for the Chinese user as the US servers would be. The break-even point is then (x-1)/x*. In other words, if the Chinese servers are four times as fast, more than 3/4 of the searches must be censored before there is a net loss of efficiency for the Chinese user who unilaterally uses the Chinese servers first..

Of course, this is all assuming the Chinese user is completely oblivious to the issue of whether her search terms will engender censored results. But i submit that well before the threshold is reached, any reasonable user will have developed some schema for determining a priori whether her search results will likely be censored. And even if the user is unable to predict that some of her searches are more likely to be censored than others, by the time she reaches the threshold she will know to run all her searches on US servers anyway. Combine this with the observation that Google would not be placing servers in China in the first place unless they represented some significant increase in speed (measured by x in the previous paragraph), and it is inevitable that even for the users who have to search twice to get their censored results Google's decision to restrict content in order to place servers in China is beneficial..

* i got this figure by assuming it takes on average t seconds to carry out a search using a US server and therefore t/x seconds on a Chinese server. i let p be the proportion of time a result is censored, and i compared the average times required to search based on two strategies: the first where the search is always done on a US server, the second where the search is always started on a Chinese server and then a US server is used if the results are censored. The equation i get is: t = p(t+t/x) + (1-p)t/x. The t's drop out, and p can be solved in terms of x..

Mexican Game Shows

So my Tax professor forwarded an article today about a Mexican government-run game show that gives prizes out to contestants who are selected randomly based on credit card purchases they have made. The stated intent of this program is to bring more transactions into the formal economy in such a way that the government can trace them and tax them. An article about the program can be found at http://www.latimes.com/news/printedition/front/la-fi-bigticket16jan16,0,6542441.story?coll=la-headlines-frontpage..

This sounds to me like a beautiful idea for a government to raise revenues in a non-controversial manner if it can indeed make the system work. The big thing i see right off is that this system plays to the psychology and risk-tolerant nature of the populace. A rational government would not implement such a program if it were not confident that revenues would exceed expenditures. Even ignoring the transaction costs of administering the program, this implies a negative expected value to the consumers. But as we know from the example of state-run lotteries or private casinos in our own country, some people will participate in such games of chance despite the negative expected value..

The interesting thing is that, like a lottery (or a guns-for-toys scheme), participation in this program is largely self-selecting. What are the implications of this observation, and who is opting into a program of this type? Obviously those who are making huge profits in the underground economy may well recognize that this system operates to their detriment and thus opt out of the program to the extent they are able. The government makes no money on these people. Moreover, the government actually loses money on the honest credit card using taxpayers who opt into this system and experience a net benefit based on transactions they would have completed and taxes they would have paid anyway..

So how does the government make any money on this program? That's where the unique nature of the system comes in. The system relies on the honest and ostensibly benefit-seeking taxpayers to pressure underground merchants into compliance. This program takes advantage of a fortuitous disequilibrium in incentives, where buyers inclined to complete electronic transactions so as to enter the contest are at odds with sellers loath to allow the enhanced scrutiny of their financial records that would accompany electronic transactions. This is where competition comes in; unless cheating and corruption are completely endemic to the undground economy, compliant merchants will emerge and sales will shift toward those merchants..

Over time the market will evolve to reflect greater numbers of merchants accepting electronic transactions. The savvy or risk-averse consumers will continue to buy from underground merchants, the ones accepting credit cards will pass some of the cost along to the consumers (keeping in mind that the consumers will pay no more than their expected benefit from entering the contest, which will invariably be lower than the financial loss accruing to the merchants), and overall the government will gain revenue at the expense of the merchants. Of course, this all assumes that it is in fact possible for merchants in the underground economy to operate profitably while in compliance with the law. i don't know enough to tell whether that is indeed the case..

Board Games Part I

So as i begin writing this, there are about 20 people in the house and i am the only person not huddled around the game of Catch Phrase in the kitchen. God i hate that game. Why? Because the incentive structure of the game is misaligned. Let's begin with a description of the game. An even number of people sit around a table and alternating people are on opposite teams. A given person whom we'll designate as the "Caller" starts with an electronic device that displays a word or phrase, and the Caller has to give clues so that the Caller's team members can guess the phrase. When the team guesses the phrase, the Caller passes the device to the left, and someone on the opposing team thus becomes the new Caller. The device has a built-in timer, and the team holding the device at the end of the time loses a point. What's wrong with this picture?

First, assuming you know how long the timer goes, you as the Caller can sit on the device thinking of the best clues to give your teammates, wait until time is almost out, and get your team to guess the phrase just in time to pass the device and stick the other team with the hot potato. i have been assured by proponents of the game that the time is not standard, but if you can come up with even a reasonable model for the time distribution the analysis still applies. On top of that, my empirical analysis after five trials indicates the time alloted by the device ranges between 53 and 58 seconds. This is almost certainly a small enough window to make the foregoing strategy viable..

On top of this, the mechanism of distributing points actually provides a distorted measure of each team's skill in giving clues and guessing phrases. Consider: if the teams are evenly skilled, you expect the teams to get approximately the same number of points, right? And wouldn't you expect a better team to score more points in general? Well, given the structure of this game, that could all depend on the distribution of the time it takes each team to guess a phrase. Assume for the moment that the team in initial possession of the hot potato alternates with each round. i invite you the reader to verify mathematically that, while there is no random distribution that gives an advantage to the weaker team (defined as the one that takes more time on average to guess its phrase), there are countless distributions that give no advantage to the stronger team either. What this means of course is that Catch Phrase is ultimately more a game of chance than of skill, unless we count sabotaging the timing of the game to be a skill..

On the other hand, let's assume that the team stuck with the hot potato at the end of a round must start with it the following round (which is how i've seen the game played in practice). Now what if one team always takes exactly 10 seconds to guess its phrase and the other team always takes 50 seconds. Now despite being "five times as good" (if such a thing can be quantified), when the 10-second team starts with the hot potato it will lose 100% of the points in the game, assuming the duration of a round always falls between 53 and 58 seconds. i have thus constructed a scenario in which a team that is substantially better than the other can nevertheless lose with 100% certainty. Surely this renders the game fundamentally flawed..

Taboo, i should mention, is the game Catch Phrase was meant to be. What makes Taboo a better game? Not only is it more challenging because you are presented with a list of words you are not allowed to use in your description, but it actually serves to measure what it purports to, namely each team's skill at giving clues and guessing the phrase. In Taboo, each team is given the same amount of time within which to guess as many phrases as it can, and points are equal to the number of phrases guessed in the allotted time. Thus the final score, the scale by which we measure which team is better, is a fairly accurate measure of the two teams' relative skill levels. Isn't this what we should prefer? After all, which of the following makes more sense: a football game where the winner is determined by how many touchdowns are scored, or a football game where the winner is determined by who has possession of the ball at the end of the game?

My next post on the subject will explore the games of Pit and Risk..