The theme of fairness has come up in very different contexts since my reading recently shifted away from being strictly thesis-centered. Of course, life isn’t fair and what is perceived as fair differs from person to person. That said, I have often wondered whether greater fairness is a hallmark of a more sophisticated or merit-driven society in the sense that hard work is more likely to be rewarded in such societies, while benefits based on, for example, sex, race or family ties may be harder to come by. The results I recently came across considered fairness in e-commerce, sports and food.
In online marketplaces and ads
I first heard about this when I had the opportunity to briefly chat with Cliff Stein (perhaps best-known for CLRS) in March about his current research. One of the things they are looking at (as I understood it) considers a situation where an advertiser is provided with some sort of guarantee that it will be treated fairly over some period of time with regards to, say, the number of times its ads are displayed, compared to the ads of competitors. (Alternatively, advertisers may have the option of buying certain tiers of service, which imply that it will receive a certain amount of preference.) The complications in this case arise from the fact that different advertisers may have specified different keywords for their products and that it is not known how many further users will enter the system before the end of the time period. (A 2010 paper developing online algorithms along these lines may be found here.) A similar situation holds in online marketplaces, where a manufacturer/seller may be interested in the number of times its products are listed as one of the first three products returned by a search for certain keywords, with the additional consideration that users who quickly find relevant information are more likely to use a marketplace repeatedly, so satisfying promises to sellers must be balanced against showing users relevant search results.
In a recent talk at the lab, Stephan Ballot, head of product at OLX, mentioned that they decided to display most recently listed ads first, while giving some preference to ads with pictures, as these lead to more sales. This solution attempts to elegantly sidestep many of the intricacies of the problem, yet the question remains whether it is ‘fair’ to sellers that someone who posts their advertisement at 02:00 may never be listed among the top results due to the high number of ads posted every morning, while someone posting an identical ad at some other time of the day may be at the top of search results for quite some time.
In determining cricket outcomes
As all cricket followers known, the Duckworth-Lewis method of adjusting scores in rain-interrupted matches has been used since 1999. This method adjusts targets based on the amount of resources (measured in overs and wickets remaining) that the chasing team has left. The general consensus in the cricketing community seems to be that it does this fairly well, however, some questions arise whent these adjusted targets are used to determine the outcomes of matches (if you are ahead of the adjusted target when the game ends, you are declared the winner).
A paper by Bandulasiri entitled Predicting the winner in One Day International cricket considered 105 uninterrupted ODIs and compared the Duckworth-Lewis predicted outcomes after 30 and 40 overs have been faced by the chasing side to the actual outcome. It found that after 30 overs D/L correctly predicted the outcome of the match only 36.27% of the time, while it predicted the correct winner after 40 overs 52.2% of the time.
Its slightly embarrassing that a game with 2.5 billion fans around the world will do better to decide rain-interrupted games by simply flipping a coin.
In food (and many other things)
I’ve long been a fan of the following technique of dividing a cake fairly: Make a cut from the centre of the cake to an edge. Assemble the interested parties. Slowly rotate a knife from the cut around the centre until a person shouts stop – cut the cake at that position and hand it to the person who stopped you. Repeat until there is no cake left. The wonderful thing about this technique is that everyone thinks everybody else received less than their fair share and that they themselves received a fair share of the cake. (In writing this piece I’ve found that this is called the Dubins-Spanier algorithm and that it guarantees every one of n people to receive a piece he/she values to be worth at 1/n of the whole.)
If anyone is particularly interested in the literature on cake cutting (which is larger than you’d think, since much of it generalises to the fair division of dividable resources, for example dividing the cost of pollution between nations) a recent survey Cake cutting – not just child’s play may be a good place to start.
I think fairness is one of those things which are broad enough to ensure that someone will always feel they are being treated unfairly. This should not prevent us from seeking provably fair policies in the application and design of technology, nor in everyday life.
Did you recently notice any results regarding fairness?