<i>John likes vanilla best, while Jane prefers chocolate. The ideal split is obviously for John to get the vanilla half and Jane the chocolate half. But if John is the cutter, then unless he knows Jane’s preferences, that ideal split will appear too risky to him: He could lose the entire vanilla half.</i><p>Given that the introductory commentry is about a couple in an intimate relationship, surely by the stage you're that invested in the cake, you should know the other person's preference. Or, crazy thought, I know, the person doing the splitting can <i>talk to the other party</i> about their preferences. "Hey, I know I'm cutting the cake, but I prefer vanilla - do you have a preference?" would solve the problem at hand in a few seconds.<p>It's also an example that doesn't feed into the Fair Buy-Sell algorithm (which looks nice for the right circumstances - indivisible items where parties can trade other items of worth (like money) and the parties are not particularly concerned for the welfare of each other). How would you do the 'Fair Buy-Sell' for the cake situation? "This cake is worth X to me and Y to you" means what, exactly?