EVALUATING ALLOCATIONS OF FREEDOM

EVALUATING ALLOCATIONS OF FREEDOM Itai Sher University of Minnesota Conference on Normative Ethics and Welfare Economics Becker Friedman Institute University of Chicago October 24, 2014

Conflict of Freedoms You and your neighbor, suppose, are at variance: he has bound you hand and foot, or has fastened you to a tree... it is on account of what you have been made to su er by the operation which deprives you of [your liberty] that the legislator steps in and takes an active part... He must either command or prohibit... he therefore cuts o on one side or the other a portion of the subject s liberty. (Bentham 1782)

Main Points Freedom must be evaluated in interactive settings where actions of some restrict freedoms of others.

Main Points Freedom must be evaluated in interactive settings where actions of some restrict freedoms of others. Two sources of the value of Freedom: Instrumental component (supplied by the agent s preferences): Freedom allows flexibility to adapt decisions to new information/contingencies. Intrinsic component (depending on value judgments about importance of basic freedoms) Certain basic freedoms are important in a way that is relatively insensitive to preferences. I provide a formal model capturing all these elements. It is hybrid: It founds evaluation of freedom on both an instrumental and an intrinsic component in an interactive setting.

Instrumental Freedom in a Decision Ann faces menu M = {option 1, option 2, option 3, etc.} Today, she does not yet know what she wants. Tomorrow, she will learn what she wants and choose. Value of M today = Ann s expected utility today given that she will choose according to her desires tomorrow. This is the instrumental value of Ann s freedom in M. Value of freedom derives from value of flexibility: Koopmans 1964, Kreps 1979, Arrow 1995, Dekel, Lipman and Rustichini 2001.

Instrumental Freedom in a Social Interaction Today, two agents do not yet know what they will want tomorrow. Tomorrow they will make decisions. The decision that each agent makes a ects the options of the others. How do we evaluate the freedom inherent is such an interaction?

Instrumental Freedom in a Social Interaction A bicycle allows Ann to go to store or theater. Ann owns bicycle ) Ann s menu = {stay home, store, theatre}. She will learn where she wants to go tomorrow morning. But suppose Ann and Bob share the bicycle With probability 1/3, when Ann seeks the bicycle in the morning, Bob has already taken it. So Ann s e ective menu = home, store with prob 2 3, theatre with prob 2 3 Any behavior for Bob (a probability he takes the bike) determines a menu for Ann. Any behavior for Ann determines a menu for Bob. Measure the values of their freedoms by their expected utilities the night before (which depends on their behavior).

Problems with Instrumental Conception of Freedom 1 If someone else cares more about controlling my personal sphere than I do, would that justify transferring my control rights to them?

Problems with Instrumental Conception of Freedom 1 If someone else cares more about controlling my personal sphere than I do, would that justify transferring my control rights to them? 2 All citizens in subpopulation S support and would never criticize government; Citizens in subpopulation C are critical of the government. They will not change their minds, and S and C are identifiable on the basis of observable characteristics. Would it then be a matter of indi erence (or close to indi erence) to amend the law that allows everyone to criticize the government so that only citizens in C can criticize the government?

Valuing Intrinsic Freedoms Diversity measures (Nehring and Puppe 2002). Attributes A: criticizing the government, celebrating Christmas, eating a vegetarian meal,

Valuing Intrinsic Freedoms Diversity measures (Nehring and Puppe 2002). Attributes A: criticizing the government, celebrating Christmas, eating a vegetarian meal, Many actions may share an attribute: criticize government while delivering introductory economics lecture criticize government while someone else tries to give an unrelated lecture criticize government in the town square

Valuing Intrinsic Freedoms Relevant attributes: Menus: criticize government support government 8 >< M 1 = >: M 2 = (M 1 ) = (support) {z } value of M 1 attend a pro-government rally, praise government, go for a walk attend pro-government rally, attend anti-government rally (M 2 )= (support)+ (criticize) 9 >= >;

Random Attributes Properties of lotteries over outcomes: Medical care available to me with probability 1. Medical care available to me with probability at least q. Medical care available to me with at least the probability it is available to anyone else. The average probability that care for di erent ailments is available is at least q.

Freedom Measures DETERMINISTIC CASE (M) =value of menu M = sum of attribute values instantiated in M = X (A) A:M\A6=; RANDOM CASE (M) =value of menu M of lotteries = integral of attribute values instantiated in M Z = (A)µ(dA) A:M\A6=;

Preference for Flexibility (M) =expected utility today to an agent that will know facts relevant to her utility when she chooses tomorrow Z X = max (z)u(z, )p(d ) 2M z = lottery (z) = probability of outcome z!

Formal Equivalence THEOREM is a menu value function for some freedom measure evaluating random attributes if and only if is the menu value function for some agent with preference for flexibility. Generalizes Nehring (1999) and Nehring and Puppe (2002) to menus of lotteries (rather than lotteries over menus)

Substantive Inequivalence INFORMATIONAL REQUIREMENTS PREFERENCE FOR FLEXIBILITY Knowledge about likelihood that agents will have various preferences tomorrow and how agents trade-o these possibilities today. FREEDOM MEASURE Judgments about the value of having access to options with certain attributes

Hybrid Measure PROPOSITION Let (M) be an overall measure satisfying (*) : ( M +(1 - )M 0 )= (M)+(1 - ) (M 0 ), and depending only on instrumental and intrinsic values. Specifically: 1 (M) 6 (M 0 ) and (M) 6 (M 0 ) ) (M) 6 (M 0 ) Then there exists 2 (0, 1) such that can be written as: (M) = (M)+(1 - ) (M) Formally identical to a result of Kochov (2007), which follows from De Meyer and Mognin (1995) generalizing Harsanyi s aggregation theorem. 1 With a strict inequality in the consequent whenever there is a strict inequality in the antecedent.

Value of Life Menu M = {(r 1, w 1 ),...,(r n, w n )}, ri = mortality probability w i = wage

Value of Life ri = mortality probability Menu M = {(r 1, w 1 ),...,(r n, w n )}, w i = wage Attribute A(q) = agent survives with probability at least q

Value of Life ri = mortality probability Menu M = {(r 1, w 1 ),...,(r n, w n )}, w i = wage Attribute A(q) = agent survives with probability at least q All attributes A(q) have same value (normalized to 1) (A(q)) = 1, 8q... but if M has A 2 3, M must also have A 1 2.SoM gets credit for both. (M) = max (1 - r) = maximum available survival probability {z } (r,w)2m intrinsic value R R Formally: (M) = (A)µ(dA) = (A(q))dq = max (1 - r) A:M\A6=; q:m\a(q)6=; (r,w)2m

Value of Life u 1 10, w h > u 1 10, w m = u 0, w ` ; w h > w m > w `

Value of Life u 1 10, w h > u 1 10, w m = u 0, w ` ; w h > w m > w ` M (M) M 1 : 1 10, w h, 0, w ` u 10 1, w h +(1- ) M 2 : 1 10, w h u 10 1, w h +(1- ) 10 9 M 3 : 0, w ` u 0, w ` +(1- )

Value of Life u 1 10, w h > u 1 10, w m = u 0, w ` ; w h > w m > w ` M (M) M 1 : 1 10, w h, 0, w ` u 10 1, w h +(1- ) M 2 : 1 10, w h u 10 1, w h +(1- ) 10 9 M 3 : 0, w ` u 0, w ` +(1- ) Agent indi erent between M 1 and M 2 ; prefers both to M 3. The hybrid measure prefers M 1 to M 2,andmaypreferM 3 to M 2. To impose a mortality risk of 1 10, (given status quo 0, w ` ), we must compensate the agent by more than w m - w `.... because we not only harm the agent, we rob her of her liberty.

Is Hybrid Measure Paternalistic? does not want to restrict choice: M M 0 ) (M) 6 (M 0 ).

Is Hybrid Measure Paternalistic? does not want to restrict choice: M M 0 ) (M) 6 (M 0 ). disagrees with agent on some menu rankings (barring a taste for freedom).

Is Hybrid Measure Paternalistic? does not want to restrict choice: M M 0 ) (M) 6 (M 0 ). disagrees with agent on some menu rankings (barring a taste for freedom). more resistant than agent to eliminating options: Agent indi erent 1 between 10, w h, 0, w ` 1 and 10, w h,but prefers larger menu. always prefers to allow agent to choose between menus: (M 1 [ M 2 ) > max{ (M 1 ), (M 2 )} (and, in an interactive setting, between mechanisms); only opposes that a smaller menu is imposed by someone else...... but this presupposes we do not care about an agent restricting her own freedom: we evaluate agent s freedom only ex ante over a lifetime or over some fixed period or interaction... what the agent gives up is her responsibility...

Social Interaction = rules of the game governing social interaction. = behavior (strategies) Depending on relevant facts i that each player i discovers before play.

Social Interaction = rules of the game governing social interaction. = behavior (strategies) Depending on relevant facts i that each player i discovers before play. M i (, -i) = equilibrium menu = outcomes/lotteries i can e ectively choose given others behavior -i In bicycle sharing game: if Bob s decision executed before Ann s, and if Bob takes bicycle with probability (depending on Bob ), Ann s menu is: {home, store with prob (1 - ), theatre with prob (1 - )}

Measuring Freedoms in Interactions ˆ (, ) = hybrid measure of freedom for social interaction (, ) (, )+(1 - )( 0, 0 ) = result of playing using strategies with probability, and 0 using strategies 0 with probability 1 -. PROPOSITION Suppose that ˆ ( (, )+(1- )( 0, 0 )) = ˆ (, )+(1- )ˆ ( 0, 0 ). If ˆ depends positively and only on the intrinsic and instrumental freedoms of each of the agents, then ˆ can be written as: ˆ (, )= X i i (M (, -i )) - apple X w i c i (M (, -i )), i2i i2i {z } {z } utilitarian welfare costs of rights violations w where c i (M) = i (All Options)- i (M),

Trade of Control in the Personal Sphere Two decisions must allotted among Ann and Bob: 1 What color shirt should Ann wear? and 2 What color shirt should Bob wear?

Instrumental Preferences Possible colors: red or green Each prefers specific shirt color for herself, and specific color for other. All four preferences equally likely. Agent i s utility = 1 (if i wears her favorite shirt color) + i (if other wears shirt i prefers for other).

Intrinsic Values Intrinsically important for an agent to be able to control her own shirt color (i.e., her own personal sphere).

Intrinsic Values Intrinsically important for an agent to be able to control her own shirt color (i.e., her own personal sphere). Appendix

Mechanisms CORRECT ENDOWMENTS (C) Each agent endowed with her own decision: control of her own personal sphere. INCORRECT ENDOWMENTS (I) Each agent endowed with other s decision: control of other s personal sphere. TRADE (T) Agents may trade control rights. NO TRADE (N) Agents may not trade. 4 possibilities: CN, IN, CT, IT

Access to Personal Sphere Agent has access to her personal sphere if either: 1 She is endowed with right to control her own shirt, or 2 Other agent willing to trade this right to her.

Access to Personal Sphere Agent has access to her personal sphere if either: 1 She is endowed with right to control her own shirt, or 2 Other agent willing to trade this right to her. Appendix

Only Bob Intrusive Suppose only Bob intrusive: (Bob prefers to control Ann s personal sphere) IT (Incorrect endowments with trade) and IN (Incorrect endowments with NO trade) lead to same outcome: Each chooses other s shirt. (Intrusive Bob not willing to trade) But IT is preferred to IN because: In IN, neither agent can control own shirt. In IT, Bob has access to control to his own shirt because Ann is willing to trade it to him. Freedom measure evaluates procedural aspects and not just outcome...... but it ignores some potentially relevant aspects: e.g., why Bob can control his personal sphere: Because he was endowed with the decision or because Ann is willing to grant him the decision.

Both Ann and Bob Intrusive Suppose Both Ann and Bob are intrusive. IT is indi erent to IN (same outcome and neither allow control over personal sphere)

Both Ann and Bob Intrusive Suppose Both Ann and Bob are intrusive. IT is indi erent to IN (same outcome and neither allow control over personal sphere) CT (Correct endowments with trade) is the unique best outcome leads to preferred outcome control of other s shirt (after trade) but allows both right of access own personal sphere. = consequentialist benefit of controlling other s (as opposed to own) personal sphere. large ) IT and IN preferred to CN small ) CN preferred to IN and IT.

Conflict with Pareto Criterion Taking intrinsic freedom seriously leads to conflict with Pareto criterion: Unanimously preferred arrangement my allow less freedom. See Sen 1970, Gibbard 1974, and others. Objection: Just allow everyone consent (as in CT) and the problem is solved.... but the intrinsic importance of consent often ignored in formal analyses is highlighted, and Unanimity is a limiting case, where interests do not even need to be traded o : Conflict with Pareto strongly suggests conflict between freedom and welfare more generally.

A Schema for Evaluating Pareto DECOMPOSITION FOR PARETO CRITERION: 1 When all relevant considerations favor policy X over policy Y, policy X should be preferred. 2 Relevant considerations = preferences of individuals concerned. Pareto = 1 + 2. When other considerations important freedoms, rights, personal and social obligations fairness these must be weighed against personal preferences.

Conclusions Freedom not only instrumentally important but intrinsically valuable. Social arrangements should balance consequences against putting decisions in proper hands.

Conclusions Freedom not only instrumentally important but intrinsically valuable. Social arrangements should balance consequences against putting decisions in proper hands. QUESTIONS How should we think about a person restricting her own freedom? Does the source of opportunity matter? How should we think (formally) of di erently rating opportunities that arise or are prevented through di erent social sources? Are value judgments about intrinsic freedoms primitive, or generated (at least in part) by a deeper normative theory? If the latter, how much guidance can the theory provide on substantive weights to be placed on di erent freedoms?

APPENDIX

Social Interactions Recall that agent i only learns facts i relevant to her choice on the morning of interaction (distributions of i are independent across i)

Social Interactions Recall that agent i only learns facts i relevant to her choice on the morning of interaction (distributions of i are independent across i) Social interaction consists of: Rules of the game potential actions for each player + mapping from actions to outcomes. Behavior: Strategy i = i s plan the night before of what action to choose the following morning as a function of i = list of strategies for all agents -i = strategies for all agents but i. M(, -i ) =menuconsistingofthee ective(random)consequencesof choosing each of her actions holding fixed everyone else s strategy. In bicycle sharing game, if Bob s decision executed before Ann s, then if Bob takes bicycle with probability (depending on Bob ), Ann s menu is: {home, store with prob (1 - ), theatre with prob (1 - )}

Intrinsic Values Intrinsically valuable to be able to control my own shirt color. Attributes I can bring it about that I wear a z-color shirt with probability at least p are valuable. Intrinsic value of menu M = maximum attainable probability of green for my shirt + maximum attainable probability of red for my shirt i (M) = X z i 2{g,r} max 2M i (z i )

Timing for Trade 1 Each agent privately learns own preferences over red and green shirts (for both agents). 2 Both agents simultaneously choose trade or no trade. 3 (A) If both choose trade, each agent makes shirt decision with which other agent was initially endowed. (B) Otherwise, each agent makes shirt decision with which she herself was initially endowed. An agent selects trade i she prefers the decision with which she was not endowed (depending on whether i > 1). This is consistent with BNE.

Only Bob Intrusive Suppose only Bob intrusive: Bob > 1 but Ann < 1. IT and IN lead to same outcome: Each chooses other s shirt.

Only Bob Intrusive Suppose only Bob intrusive: Bob > 1 but Ann < 1. IT and IN lead to same outcome: Each chooses other s shirt. But IT is preferred to IN because each agent s menu in IN is: M Yours i = but in IT Bob s menu is: Other wears green shirt and I wear each color with prob 1 2, Other wears red shirt and I wear each color with prob 1 2 M choice = MBob Mine [ MYours Bob since Ann is willing to trade with Bob. Freedom measure evaluates procedural aspects and not just outcome...... but it ignores some potentially relevant aspects: e.g., why Bob can control his personal sphere: Because he was endowed with the decision or because Ann is willing to grant him the decision.

Only Bob Intrusive Suppose only Bob intrusive: Bob > 1 but Ann < 1. IT and IN lead to same outcome: Each chooses other s shirt. But IT is preferred to IN because each agent s menu in IN is: M Yours i = Other wears green shirt and I wear each color with prob 1 2, Other wears red shirt and I wear each color with prob 1 2 but in IT Bob s menu is: M choice = MBob Mine [ MYours Bob since Ann is willing to trade with Bob. Freedom measure evaluates procedural aspects and not just outcome...... but it ignores some potentially relevant aspects: e.g., why Bob can control his personal sphere: Because he was endowed with the decision or because Ann is willing to grant him the decision. Back

Only Bob Intrusive = Bob s benefit if he control s Ann s personal sphere (rather than his own) minus Ann s loss if this is so is instrumental/consequentialist.

Only Bob Intrusive = Bob s benefit if he control s Ann s personal sphere (rather than his own) minus Ann s loss if this is so is instrumental/consequentialist. Whether CT which is superior in freedom (both agents have the option retain control over their personal sphere) is overall superior to IT depends on magnitude of. Rights traded o against consequences.

Both Ann and Bob Intrusive Suppose Both Ann and Bob are intrusive: Bob > 1. IT is indi erent to IN Ann > 1and (same outcome and neither allow control over personal sphere)

Both Ann and Bob Intrusive Suppose Both Ann and Bob are intrusive: Bob > 1. IT is indi erent to IN Ann > 1and (same outcome and neither allow control over personal sphere) CT is the unique best outcome leads to preferred outcome for both and allows both right of access own personal sphere.