Distribution of jointly owned private goods by the demand-revealing process: Applications to divorce settlements and estate administration
In this concluding section, we summarize the workings and outcomes of our versions of the demand-revealing process, followed by summaries of the advantages and disadvantages of these versions applied to the problem of the distribution of private goods among individuals who jointly own or have claims against the goods. Finally, we briefly discuss two alternatives to our versions of the demand-revealing process. As discussed in Section 2, the demand-revealing process elicits honest value revelation by separating the individual's stated valuations of a good from the price or tax he must pay for the good. In the problems we consider, wherein the parties jointly own the goods, we must also separate the amount of cash received by each party from his stated valuations. By inducing the parties to honestly reveal their valuations, the process is able to efficiently distribute goods to the parties placing the greatest values on them. The net benefits in this process, which result from the excess of the value of items received by the parties involved over the price paid for those items plus the cash distributed among the parties involved, are generally distributed in approximately the desired proportions. In order to accomplish honest value revelation and the other desirable properties stated above, there is a necessary cost in the form of a waste in the demand-revealing process similar to the Clarke tax. However, users of the process could be compensated for their expected waste from a fund established for that purpose. The major advantage of the process specified in this paper is the honest revelation of values which results in efficiency in the distribution of the property, while approximately achieving the desired overall division of the property. As long as the parties do not collude in their value revelations, one can expect values to be honestly revealed by the parties involved. A second advantage is that the process requires no personal interaction, as do other approaches to distribute property, such as direct negotiation among the parties or an auction. This depersonalization may be quite desirable when personal conflicts may be involved. The disadvantages of the process include that waste is involved (which tends to diminish but does not disappear as the number of parties increases), that the desired overall distribution of property may only be approximated ex post, that ‘spiteful’ bidding may occur, and that strategic misstatement of valuations may occur if subsets of individuals collude. An example of spiteful bidding would be the case where party 1 values an item highly and bids accordingly. Party 2 could be aware of party 1's high valuation of the item and overstate her own valuation (V 2 ). This results in a small risk to party 2 that her bid may prevail, but party 2 may feel the risk is worth the higher price that she is forcing upon party 1. Although spiteful bidding is possible, and can create inefficiency and waste, this sort of behavior would probably be even worse in other processes such as an English auction. Collusive strategic behavior by subsets of individuals is possible, as it is with other versions of the demand-revealing process. Somewhat surprisingly, however, collusive strategic behavior under this version of the demand-revealing process is unlikely to result in inefficiency in the distribution of items, and, in fact, can reduce waste. It can also, however, reduce the net benefits of non-members of the coalition. 11 Given the waste involved in the process presented in this paper, one may wish to explore alternative processes which can be applied to similar economic problems. Two such alternatives are very briefly discussed here. A version of point voting suggested by Mueller, Tollision and Willett (1974) was applied to achieving a desired level of ex post equality in results over a number of issues in an election. Applied to our problem, this process would begin with an equal number of points being distributed to each party and allowing each party to allocate points among items as he desires, with each item tentatively distributed to the party allocating the most points to it. Depending upon the distribution among the parties of the point values of the items received, the points allocated to each party are adjusted and items redistributed. This process continues until approximately the desired proportions of the total property are received by each party (in terms of the original point allocations made by the parties). Such a process could be handled quite easily by computer once the various parties had stated their relative valuations of the items. The advantage of such a process would be that there would be no waste as in our version of the demand-revealing process. The disadvantage is that the process is more complex than the demand-revealing process, it excludes outside bidders, and it is subject to strategic voting in the parties' allocations, which can result in inefficiency. A second alternative which avoids the waste of our process is to use the demand-revealing process with the parties bidding with points rather than with dollars. Points could be allocated among the parties in accordance with the distribution desired, and then the parties could use these scarce points with which to bid. Although such a process would avoid the waste of our process, it is somewhat more complex than our process, in that points are used for bidding rather than people merely stating their valuations, it excludes outside bidders, it may not approximate the desired ex post shares for the parties involved, 12 and efficiency may not be achieved. 13 In light of its advantages and the absence of alternatives which can avoid its disadvantages without incurring further problems, we feel that the specific applications of the demand-revealing process suggested in this paper could be of practical use in some instances in divorce settlements or estate administration, or in private goods decisions problems of a similar nature wherein the goods are being distributed among their joint owners. For example, the process could be used in the distribution of property in a partnership dissolution. The applicability of the demand-revealing process to these various problems is further evidence of the broad usefulness of the demand-revealing process for improving the efficiency in public and private goods decisions. There are only three forms of profitable collusion under this process. One is for parties 1 and 2 colluding by understating V 2 to reduce the price paid by party 1 (yielding a maximum net gain to the coalition of V 2 −V 3 If V 2 is stated as equal to V 3 ). The second is for parties 2 and i (i ≥ 3) colluding by overstating V i as V 2 in order to increase the cash received by party 2 (yielding a net gain to the coalition equal to w 2 (V 2 −V 3 )). Neither of these forms of strategic collusive behavior results in inefficiency in the distribution of the item, and, in fact, each can reduce waste since waste equals (w 1 + w 2 )(V 2 − V 3 ) and these strategies can reduce the stated difference between V 2 and V 3 . The strategic voting can benefit the coalition, somewhat at the expense of the other parties, however, as in the preceding example. A third form of collusion is for party 2 to collude with party i (i ≥ 3) to overstate V 2 in order to increase the cash received by party i. Such a strategy can yield benefits for the coalition approaching w i (V 1 − V 2 ). The danger exists, however, that party 2's stated valuation may exceed V 1 , in which case party 2 would receive the item at a price exceeding its true valuation. This would be inefficient, and would increase waste since (w 1 + w 2 ) (V 2 − V 3 ) would increase, unless part of the strategy was a corresponding increase in V 3 . The possibility under this strategy of receiving an item at a price exceeding its worth seems to make this collusive strategy less likely than the other two, and thus, inefficiency due to collusive strategy does not appear to be a serious problem. Copyright Martinus Nijhoff Publishers 1985
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