Voting and the Scale-Free Theory of Intelligence

Arrow’s impossibility theorem ¹ (and its stronger forms ²) shows that no ranked voting system can satisfy all of Kenneth Arrow’s five axioms for rational collective choice. At first glance, this seems to deny the very possibility of rational group decision-making, and some even misinterpret the theorem as suggesting that democracy itself is impossible ³.

I discuss below some important insights from Arrow’s theorem. These are mostly drawn from ⁴ and ^{5 6}, not my own novel contributions. I then consider how these insights connect to the idea of a scale-free theory of intelligence — the conjecture that fundamental principles may govern both individual minds and large-scale systems like societies ⁷.

Arrow’s theorem overlooks the most important part of rational group decision-making. In social choice theory, a “decision” is defined as choosing among fixed options, based on fixed and consistent preferences. However, the preferences are not fixed! Before one decides who to vote for, one has to consider which policies of different parties appeal to them most and how it matches with their own political ideology. The political parties themselves constantly tinker their manifestos and messaging based on ground feedback, which often leads to changes in voter preferences. Hence, at the heart of decision making is communication between parties and voters, which leads to the creation of new ideas and modification of existing ones. Only at the end of this process does one select their preferred candidates, and the relevance of Arrow’s theorem comes into picture.

In other words, social choice theory is based on false assumptions about what “deciding” consists of. It is mistaking an abstract process that it has named decision-making for the real-life process of the same name. The fact that Arrow’s axioms lead to logical inconsistency means that Arrow’s conception of rational decision-making is itself irrational, and not that rational decision-making isn’t possible ⁴.

So what does rational group decision-making actually require? As Popper argued ^{5 6}, the right criterion to judge a political system is whether it allows the removal of bad policies and bad governments without violence or bloodshed. Unlike Arrow’s axioms, this presents a practical, technical challenge. Modern democracies provide working solutions to this challenge, with elections being just one of the institutions involved.

Now, if we conjecture that there exists a scale-free theory of intelligence — fundamental principles which simultaneously govern the designs of well-functioning minds and societies ⁷ — then insights at one scale should appear at another. For example, voting is central to democratic systems (the only political system that works, as Churchill noted). Interestingly, according to the “thousand brains theory” of intelligence, cortical columns in the brain may also use voting mechanisms ⁸. This perspective opens up exciting research directions. For example, in practice, the first-past-the-post system (used in the UK) tends to work much better than proportional representation (used in Germany) ². Should we then expect brains to use first-past-the-post voting as well? Or, if we discover a different voting mechanism in the brain, might that suggest improvements for human voting systems? (A similar example is given in ⁹, where researchers developed a more efficient distributed bipartite matching algorithm by studying neuromuscular circuits.) This also raises many other interesting questions: for example, if voting does occur in biological systems (as hypothesised in the thousand brains theory ⁸), then what is the analogue of the violence or bloodshed that arises from failures of collective decision-making in human societies? If a scale-free theory of intelligence does exist, then we should expect such an analogue to exist as well.

Finally, if we conjecture that Popper’s view of democracy ^{5 6} — rather than Arrow’s conception — better captures rational group decision-making, then we might ask: can we find parallels of Popper’s model in biological systems of voting as well? Exploring such biological analogues could provide falsifiable predictions for a scale-free theory of intelligence.