Pleb Economist #12: Stacker News and Social Choice Theory

There's been a lot of talk on zaps and downzaps lately. In particular, there seems to be an ideological tug of war between Israel supporters and critics, who are variously utilizing zaps or downzaps to try and shape the front page of Stacker News.

The question of how posts should be ordered on the front page of Stacker News (LIT) is exactly the kind of problem studied by social choice theorists.

The general form of the problem is: given a group of N individuals, each with their own preferences over items, how can we arrive at a common ordering which is shared by everyone, that somehow reflects everyone's preferences?

As I wrote about previously, the answer is: we can't. There is in fact no system that can ensure a common ordering that satisfies some basic properties of fairness and rationality. This result is known as Arrow's Impossibility Theorem.

What are some of those basic properties of fairness and rationality that we want to ensure?

Non-DictatorshipNon-Dictatorship

One of them is non-dictatorship. This means that the common ordering is not solely determined by the preferences of one individual. Stacker News does seem to satisfy this.

Pairwise Majority RulePairwise Majority Rule

Another basic principle is pairwise majority rule.^[1] That is, if the majority of participants prefers item A to item B, then the common ordering should also rank item A higher than item B. Stacker News currently doesn't seem to satisfy this, because a small set of highly motivated zappers/downzappers can boost broadly unpopular posts to the top, or shoot broadly popular posts to the bottom.

Independence to Irrelevant AlternativesIndependence to Irrelevant Alternatives

A third basic principle we might want is independence to irrelevant alternatives (IIA). This says that if the common ordering ranks A above B when C is not an option, then adding C as an option cannot reverse the relative ranking of A and B in the common ordering (regardless of where C ends up ranking). A joke about IIA, apocryphally attributed to philosopher Sidney Morgenbesser, goes like this:

Morgenbesser, ordering dessert, is told by a waitress that he can choose between blueberry or apple pie. He orders apple. Soon, the waitress comes back and explains that cherry is also an option. Morgenbesser replies, "In that case, I'll have blueberry."

It's a bit hard to assess the degree Stacker News does or doesn't satisfy IIA. But since zaps and downzaps are coming from a fixed pool, it's reasonable to assume that IIA is violated. For example, the ordering of the front page might look a certain way if there are no Israel posts, but once someone makes an Israel posts, the entire pattern of zapping may change as people direct their sats towards those posts rather than other posts.

SN AssessmentSN Assessment

To summarize, Stacker News' post ranking system would fair as follows according to basic choice theory principles:

Ken Arrow's insight with his impossibility theorem was basically that no social ranking system can simultaneously satisfy all three of the above properties (and still always be able to rank all alternatives).

Moving Forward: Do we want to give more power to express preference intensity, or preference ordering?Moving Forward: Do we want to give more power to express preference intensity, or preference ordering?

Although this is a negative result, it doesn't mean that improvements to the functioning of the system can't be made. From my observation, the biggest critiques are that a handful of highly motivated zappers/downzappers have disproportionate influence on the rankings, in a way that doesn't concord with the preferences of the less motivated majority.

This itself highlights one of the weaknesses of the ordinal social choice framework, which is that it concerns itself only with orderings, i.e. do you like A or B better, and ignores intensity of preferences, i.e. by how much do you like A better than you like B? It is possible that SN's current system prioritizes an expression of preference intensity while weakening peoples' ability to express their preference orderings.

That's a design choice, and I don't know what the right answer is. But I just offer some of this up as food for thought, both for stackers and for @k00b and team as they continue to think through message board design incentives.

1. As a technical note, pairwise majority rule is actually a much stronger condition than is necessary. Arrow's Impossibility Theorem rules out a much greater set of voting systems than just those which are non-dictatorial, independent of irrelevant alternatives, and satisfy pairwise majority rule. ↩