Charles Plott (1973) elaborated a suitable notion of path independence. Suppose we arrive at our choice by what he called divide and conquer: first we divide the alternatives into some smaller sets—say, because these are more manageable—and we choose from each one. Then we gather together all the alternatives that we have chosen from the smaller sets, and we choose again from among these. There are many ways of making the initial division, and a choice procedure is said to be path independent if the choice we arrive at in the end is independent of which division we start with (Plott 1973: 1080). In Arrow’s account, social choices are made from some given “environment” \(S\) of feasible alternatives by maximizing a social ordering \(R\): the choice \(C(S)\) from among \(S\) is the set of those \(x\) within \(S\) such that for any \(y\) within \(S, xRy\).  It is not difficult to see how intransitivity of \(R\) can result in path dependence. Consider again the paradox of voting of Section 1.  \(A\) is strictly favoured above \(B\), and \(B\) above \(C\); but, contrary to transitivity, \(C\) is strictly favoured above \(A\). Starting with the division \(\{\{A,B\}, \{B,C\}\}\), our choice from among \(\{A,B,C\}\) will be \(\{A\}\); but starting instead with \(\{\{A,C\}, \{B,C\}\}\) we will arrive in the end at \(\{B\}\).