by John Allen Paulos
An abstract paradox discussed by Yale economist Martin Shubik has a logical skeleton that can, perhaps surprisingly, be shrouded in human flesh in various ways. First Shubik’s seductive theoretical game: We imagine an auctioneer with plans to auction off a dollar bill subject to a rule that bidders must adhere to. As would be the case in any standard auction, the dollar goes to the highest bidder, but in this case the second highest bidder must pay his or her last bid as well. That is, the auction is not a zero-sum game. Assuming the minimum bid is a nickel, the bidder who offers 5 cents can profit 95 cents if the no other bidder steps forward.
This can lead to an unexpected result. The bidder who begins with a nickel bet will likely be outbid by another bidder offering 10 cents for the dollar and thereby standing to reap a 90 cent profit if not outbid. This profit margin too would likely entice a bidder, maybe the first one, to offer 15 cents and score a profit of 85 cents. Now the bidder who bet 10 cents wants to keep from losing 10 cents and so is likely to up his bet to 20 cents. This continues as, at each stage, the bidders must wrestle with the issue of sunk costs and decide whether to give up or raise their bid for the dollar by 5 cents or more.
These bids are not irrational, but can nevertheless reach the one dollar mark. This will happen when one of the bidders bids 95 cents and another bids a dollar. The bidder offering 95 cents then faces a loss of 95 cents if he or she declines to bid $1.05. Declining may be unlikely, however, since bidding $1.05 would reduce their loss from 95 cents to only 5 cents, paying $1.05 for $1. These incentives will remain even as the bids exceed a dollar with no compelling natural limit. Second highest bidders, by definition, always lose more than the highest bidders yet gain nothing, and so always want to lessen their losses and gain something by becoming the highest bidder. Read more »


Vitamins and self-help are part of the same optimistic American psychology that makes some of us believe we can actually learn the guitar in a month and de-clutter homes that resemble 19th-century general stores. I’m not sure I’ve ever helped my poor old self with any of the books and recordings out there promising to turn me into a joyful multi-billionaire and miraculously develop the sex appeal to land a Margot Robbie. But I have read an embarrassing number of books in that category with embarrassingly little to show for it. And I’ve definitely wasted plenty of money on vitamins and supplements that promise the same thing: revolutionary improvement in health, outlook, and clarity of thought.
Sughra Raza. Shadow Self-portrait on a Young Douglas Fir, May 3, 2024.






There is a meme on the internet that you probably know, the one that goes, “Men will do x instead of going to therapy.” Here are some examples I’ve just found on Twitter: “Men will memorize every spot on earth instead of going to therapy,” “men would rather work 100 hours a week instead of going to therapy,” and “men would literally go to Mars instead of going to therapy.” The meme can also be used ironically to call into question the effectiveness of therapy (“Men will literally solve their problems instead of going to therapy”), but its main use is to mock men for their hobbies, which are seen as coping mechanisms taking the place of therapy (“men will literally join 10 improv teams instead of going to therapy”). The implicit assumption in this formula is that the best way for men to solve whatever existential problems they may have is to go to therapy. I don’t particularly like this meme, and I don’t think therapy is necessarily the best way for a man to solve his problems (although it may be in some cases), but what do I know? I’m setting myself up for this response: “men will write a 2,500-word essay about why you shouldn’t go to therapy instead of going to therapy.” Fair enough. I should specify that I don’t have an issue with therapy itself; instead, I have an issue with a phenomenon I find pervasive in contemporary American culture, which is the assumption that therapy is a sort of magic cure for any ills one may have. 
Sughra Raza. Self Portrait After Dark, Butaro, Rwanda, November 2023.
Taiwan is an independent prosperous liberal democracy of 24 million free people that the Chinese Communist Party solemnly promises to annex to its empire by whatever means are necessary. Although Taiwan’s flourishing capitalist economy once allowed it to outgun and hence straightforwardly deter China from a military invasion, this military advantage has switched to China over the last 20 years. If Taiwan is to be kept free it must find another means to deter the CCP.
