When I first ran across Landsburg's More Sex/Safer Sex argument, I thought, "That can't be right." Sure, if more low-activity players engage in hook-ups, the more likely all players will find a low-activity partner instead of a riskier high-activity partner. Nonetheless, the more sexual contacts occur with some risk, even low-risk, the more infections can occur.

Or maybe there is something unexpected happening as Landsburg claims.

Anyone who has taken courses in probability and statistics -- or has read a mathematical puzzle book -- knows how often such problems can contradict one's intuition and that it is folly to believe one can verbally argue the way to the truth in these matters.

I don't have the math to tackle this problem directly, but it's not much trouble to set up a simulation for a stripped-down Landsburg scenario and run a large population through tens of thousands of sexual contacts using weighted random functions to determine which contacts occur and of those which transmit infections.

In my simulation there is a pool of 1000 players: 100 are high-activity players who have an encounter on the average of 1 per 10 days and 900 are low-activity players, who have a sexual encounter on the average of 1 per 100 days or higher. To test Landsburg's hypothesis, this low-activity value is varied upward and the resulting number of infections for different activity values compared.

Half the high-activity players are already infected when the simulation starts. Transmissibility is assumed to be 1 per 100 sexual contacts. The simulation runs for 1000 days. A trial accumulates the results from a 100 runs.

Each day of a run the simulator calls the weighted random function for each player to determine whether to add that player to the day's hookup queue. Then all the players at the queue are paired off for one sexual encounter and their possible infection randomly determined.

It's a simple model that assumes that all players are bisexual with equal odds of infection. Each player at the hookup queue is always successful in coupling with a random partner unless the number at the queue is odd, which leaves the last player out. It is further assumed that no players have potentially unsafe sex outside the hookup queue.

Using this model, which seems to satisfy Landsburg's basic requirements, the number of infections steadily climbs as the low-activity rate is increased. I've varied the other parameters with no luck in validating Landsburg's claim that "More sex is safer sex."

According to my simulation, persuading sexual conservatives to take more sexual partners will not "slow the spread of AIDS" or "save lives" as Landsburg promises. On the contrary, it will increase the spread of such diseases.

Landsburg's analysis seems to err on the following point: although the odds for a safe encounter on a single night increase when more low-activity players join the hookup scene, the low-activity players must continue to have more encounters to maintain their higher activity rate and therefore they receive more infections over time, thereby raising the infection rate for the entire population.

For high-activity players, the increased activity of the lows is a pure boon. The number of infections among high-activity players does drop with increased activity by the sexually more restrained.

It is true, however, that the individual risk per sexual encounter does drop as low-activity players increase their activity. Since Landsburg claims that sex in itself is good, perhaps he is judging that the larger increase in sex acts more than makes up for the increased number of infections among low-activity players.

It's hard to be sure exactly what Landsburg means because his essay is vague on specifics. Landsburg is more intent on speculating how to encourage sexual conservatives to loosen their morals for the greater good, even though it is not to their individual benefit.

He does mention the importance of safe sex, i.e. condoms, and the likelihood that low-activity players will use condoms while high-activity players won't. Adjusting the simulation so that the lows always use condoms while the highs, left to their own devices, won't, actually yields the result Landsburg promises. The more sex that low-activity players have, the fewer infections occur in the entire pool.

However, in this condom scenario what is really happening is that low-activity players are enforcing safe sex on the high-activity players. So the moral of that story is something of a tautology: "More safe sex is safer sex."

Although Landsburg makes only cursory arguments for his More Sex/Safer Sex claim, he does cite a paper by Michael Kremer ( http://hoohila.stanford.edu/workingpapers/getWorkingPaper.php?filename=E-95-8.pdf ) several times as an authoritative support for More Sex/Safer Sex.

The Kremer paper contains much fierce math but in the introductory section Kremer is making a somewhat different argument than Landsburg. Kremer's article is based on a game theory model which posits that as low-activity players reduce their activity, the high-activity players will have less incentive to restrain their risky behavior and therefore increase their activity, and visa-versa: if the low-activity players increase their activity, the high-activity will reduce theirs.

So, per Kremer, I tried increasing the low-activity while decreasing the high-activity in the simulation, and the result was a bumpy stability in infections. However, it was impressive how many more sexual contacts this approach allowed while keeping the infection rate steady -- much more bang for the risk, so to speak.

Lastly, I tried the commonsense approach: lowering the activity of the high-activity players. Not surprisingly, this approach had the greatest impact in reducing infections (aside from using condoms), albeit at the cost of also reducing the number of sexual contacts.

In other words, "Less sex is safer sex." Of course, that nugget of wisdom is entirely conventional and won't generate controversy or sell books.

Please check my work and assumptions or try your own simulations. It's an interesting problem in its own right, as well as being important in this age of STDs.