Comment on Proposal Sequence Design

Though not a critical aspect of the experimental design or interpretation of results, complications introduced by the inability to measure proposals following settlement of a dispute invite side commentary on the methodology of proposal elicitation. The objective of this methodological discussion is actually substantive. The following com- mentary underscores the relative reliability of proposal and bargaining data collected under the present experimental design.

Analytical complications relating to proposal elicitation (e.g. the difference be- tween strong and weak interpretations of theoretic predictions) raise the question whether the present experimental design could be improved upon. For example, an alternative elicitation scheme with many analogues in the experimental literature would be to ask defendants to submit, ex ante, full sequences of proposals to cover the entire the duration of bargaining. With full schedules of proposals in hand at the start of bargaining, settlement would not preclude subsequent measurement of pro- posal sequences. For narrative simplicity, I refer to this as a menu design approach.

The use of a menu design approach to proposal elicitation has much to recommend it. For one thing, it would greatly simplify subsequent statistical analysis. Addition- ally, the menu design approach may tend to induce greater subject introspection. Treating the decision schedule as a cohesive problem comports with theoretic anal- ysis and may tend to clarify the implications of various strategies: e.g. that offering an increasing sequence of NPV settlement proposals may incentivize settlement delay on the part of a plaintiff.

The present experimental design eschews the menu design approach out of concern for experimental validity. An initial concern is that introducing a menu of proposals changes both the rules and information structure of the problem. It provides a defen- dant with an artificial capacity to constrain future action, and it provides a plaintiff with information on counter-factual proposals. I doubt many litigants in the field con- summate a final settlement by enumerating the actions they would have taken under various unrealized contingencies! While these concerns can admittedly be mitigated by careful structure of the bargaining environment—e.g. requesting a full menu of proposals upfront but only revealing proposals in the sequence at appropriate times in the dispute—a more fundamental concern remains.

The remaining concern attaches to the way that a menu design approach defines the decision structure of the game. Like a game of chess, the decision structure of the menu design approach is both deep (requiring repeated inductions) and wide (involving many alternatives and contingencies). Subjects’ daily lives familiarize them with decision structures which are either shallow (approximating contemporaneous decisions) or narrow (involving few alternatives); deep and wide decision structures are often alien (Norman, 1988, pp. 119–127).

The chess analogy is apposite. If placed in the role of the advantaged player near the end of a game of chess, a subject may easily win the game within a few moves—making each move in sequence, watching how the opponent responds, and then making another move. If given the same task, but instead asked to provide, ex ante, a menu of moves for every (factorial) progression of board positions until the end of play, I suspect an average subject would falter. The problem is not that the under- lying game is difficult (the subject wins without difficulty in the first hypothetical), but that the latter decision environment involves an unnatural cognitive process, and is therefore difficult. In the settlement bargaining context, as in the chess example, the menu design approach seems both artificial and unlikely to generate the more internally and externally valid data.

D

Graphical Appendix

D.1

Online Appendix

An online appendix, providing continuous-time replays of all SE1 disputes, is avail- able at_{http://people.virginia.edu/~sps2d/settlement_bargaining_replays/}or by request of the author. Experimental measurements are used to reconstruct the exact play of each game, and reconstructed games are then converted to continuos-time Shockwave Flash (*.swf) graphics files. The online appendix will be maintained by the author until the supporting technology (XHTML, JavaScript, php5, Shockwave Flash) becomes unsupported.

Illustrated below, the online appendix allows a user to watch the progression of bargaining (i.e. proposals and acceptance decisions) throughout all 600 SE1 disputes. Explicit proposals are represented by black dots, and implicit proposals are repre- sented by black connecting lines between dots. Settlement is indicated by a vertical orange line drawn at the time of agreement, and failure to settle is indicated by a vertical red line at the conclusion of the round. Context lines illustrate controlled pri- vate information: one line (labeled “E [Trial]”) indicates the expected value of a trial verdict given the plaintiff’s injury draw, while the other (labeled “Injury”) indicates the size of the injury itself. Finally, predicted proposals and settlement decisions are represented by blue (unlabeled) lines of appropriate shape.

The user can select whether units are dispayed in gross value or in net present value. Unit control is crossed with an option to overlay theoretical predictions, allow- ing for a total of 4 ways to replay each bargaining game. To protect subject anonymity, subject and session data are surpressed in the construction of bargaining-game re- plays. The order in which games are displayed is static, but has been randomized so that the sequence of replays does not reveal identifying information.