Scandinavian Working Papers in Economics

Working Papers,
Lund University, Department of Economics

No 2010:16: Budget-Balance, Fairness and Minimal Manipulability

Tommy Andersson (), Lars-Gunnar Svensson () and Lars Ehlers ()
Additional contact information
Tommy Andersson: Department of Economics, Lund University, Postal: Department of Economics, School of Economics and Management, Lund University, Box 7082, S-220 07 Lund, Sweden
Lars-Gunnar Svensson: Department of Economics, Lund University, Postal: Department of Economics, School of Economics and Management, Lund University, Box 7082, S-220 07 Lund, Sweden
Lars Ehlers: Département de Sciences Économiques and CIREQ, Université de Montréal, Postal: Montréal, Québec H3C 3J7, Canada

Abstract: A common real-life problem is to fairly allocate a number of indivisible objects and a fixed amount of money among a group of agents. Fairness requires that each agent weakly prefers his consumption bundle to any other agent’s bundle. In this context, fairness is incompatible with budget-balance and non-manipulability (Green and Laffont, 1979). Our approach here is to weaken or abandon non-manipulability. We search for the rules which are minimally manipulable among all fair and budgetbalanced rules. First, we show for a given preference profile, all fair and budgetbalanced rules are either (all) manipulable or (all) non-manipulable. Hence, measures based on counting profiles where a rule is manipulable or considering a possible inclusion of profiles where rules are manipulable do not distinguish fair and budgetbalanced rules. Thus, a “finer” measure is needed. Our new concept compares two rules with respect to their degree of manipulability by counting for each profile the number of agents who can manipulate the rule. Second, we show that maximally linked fair allocation rules are the minimally (individually and coalitionally) manipulable fair and budget-balanced allocation rules according to our new concept. Such rules link any agent to the bundle of a pre-selected agent through a sequence of indifferences.

Keywords: Minimal manipulability; fairness; budget-balance; allocation rules

JEL-codes: C71; C78; D63; D71; D78

25 pages, First version: November 26, 2010. Revised: January 15, 2013.

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