Abstract
Republican and so-called independence conceptions of freedom stand out from other conceptions by embedding strong modal conditions on what it takes for a person to count as being free to do something. For this reason, the extent of one’s freedom, conceived under republican/independentist lights, cannot be measured by any of the measures of freedom that have been developed so far in the literature on freedom, since these do not register the requisite modal constraints. In this paper I propose a measure of freedom that does capture the requisite modal concerns. I do so by relying on work in the semantics of counterfactuals to define a measure of how modally robustly available an option is to an individual.
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Notes
The reader might protest that not every theory of counterfactual semantics postulates a tetradic similarity relation. Most only postulate a binary similarity relation. This is true, but the binary relations that are generally postulated already define certain tetradic similarity relations. So I am not assuming more than anyone’s view already implies. For example, Lewis postulates a binary ordering relation for every possible world, noted \(\trianglelefteq _i\), where i is the world in question. Given this family of orderings, one can stipulate that if \(w_1\trianglelefteq _1 w_2, w_3\trianglelefteq _3 w_4, w_2\bowtie _1w_3,\) and \(w_1\trianglelefteq _3w_4\), then \((w_1,w_2)\trianglelefteq (w_3,w_4).\)
Note that d is always defined because any subset of N is bounded because N itself is bounded, and therefore the set of boundary points of any subset of N is a closed and bounded set. And since any closed and bounded set has an element least distant from 0, there is a boundary point nearest to the origin.
Note that the distinction between a particular option and an opportunity set roughly maps on to the distinction Carter (1999) draws between specific freedoms and overall freedom. A specific freedom is the freedom to do some specific thing, e.g. eat an apple strudel and then do handstand, while overall freedom refers how all the specific freedoms each person enjoys aggregate to determine who is freer than whom, in a general sense. In our setup, an option is a specific freedom, and the ranking of opportunity sets is the overall freedom ranking.
Formally speaking, these two requirements amount to just one requirement, namely, that overall freedom be strictly increasing in the membership grade of each option: i.e., given (X, m), (X, f), if \(m(x)\ge f(x)\) for all x, then \((X,m)\succsim (X,f).\) If, moreover, there is an x such that \(m(x)> f(x)\), then \((X,m)\succ (X,f).\)
Formally: given four opportunity sets (X, m), (X, f), (X, g), (X, h), if \(m(x)=f(x)\iff g(x)=h(x)\) and for any x such that \(m(x)\ne f(x), m(x)=g(x)\iff f(x)=h(x)\), then \((X,m)\succsim (X,f)\iff (X,g)\ge (X,f).\) This property effectively guarantees, given completeness and a technical assumption of continuity, that the ranking of individual freedom can be represented by an additive function.
Formally, this amounts to a symmetry requirement: given (X, m), (X, g), if there is a map \(\sigma \) from X to itself such that \(m(x)=g(\sigma (x))\) then \((X,m)=(X,g).\)
Indeed, well-known results from social choice theory establish that a separable, complete, symmetric, complete, continuous, and monotonic preorder over a finite set of more than two objects is representable by a real-valued function which is decomposable into a sum of non-convex functions over each of its arguments [see Blackorby et al. (2005, Ch. 4) for rigorous formal treatment, or Hirose (2014, Ch. 2) for more intuitive discussion]. The rule I propose only assumes the special case in which these functions are in addition non-concave.
Granted, I don’t know how much divergence I would expect between the robustness of the freedom to \(\phi \) and the improbability of my being prevented from \(\phi \)-ing. The modal robustness of a property and its chance of being observed are not independent: for example, if it’s impossible to prevent me from drinking tea, then the probability that I will be prevented from drinking tea is zero, and my freedom to drink tea is maximally robust. Thus, although robustness and probability can in principle come apart, it might be that my republican measure of freedom and Carter’s liberal measure of freedom end up converging in most actual cases.
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For their insightful comments and feedback, I would like to thank Alex Voorhoeve, Campbell Brown, Ralf Bader, Bob Sugden, John Weymark, Alan Háyek, two anonymous reviewers, and audiences at the LSE’s Choice Group and the 2021 CPA. Thanks also to Philip Pettit, for many helpful conversations that helped me develop my ideas.
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Côté, N. Measuring republican freedom. Synthese 200, 486 (2022). https://doi.org/10.1007/s11229-022-03964-9
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DOI: https://doi.org/10.1007/s11229-022-03964-9