That sounds familiar to the various voting systems that satisfy the Condorcet criterion (basically, ignoring all votes for other parties, do people prefer A to

That sounds familiar to the various voting systems that satisfy the Condorcet criterion (basically, ignoring all votes for other parties, do people prefer A to B?). There are a lot of different ways of picking a winner when two or more candidates are tied under Condorcet -- ranked pairs, beat paths, etc, including rules like the one you suggest. But in voting systems, Arrow's Theorem says none of those methods can be truly satisfactory, at least if you accept Arrow's list of requirements. Similarly for Olympics ranking, I don't think any method for breaking ties will be able to satisfy all the requirements of a good ranking (e.g., removing a country from competition shouldn't change any other rank orderings). So personally I don't think any of those tie-breaking methods really have any meaning. You might as well just toss a coin.