Skip to main content
×
×
Home

Impossible by design? Fairness, strategy, and Arrow’s impossibility theorem

  • Christopher McComb (a1), Kosa Goucher-Lambert (a1) and Jonathan Cagan (a1)
Abstract

The design process often requires work by teams, rather than individuals. During team based design it is likely that situations will arise in which individual members of the team have different opinions, yet a group decision must still be made. Unfortunately, Arrow’s impossibility theorem indicates that there is no method for aggregating group preferences that will always satisfy a small number of ‘fair’ conditions. This work seeks to identify methods of combining individual preferences that can come close to satisfying Arrow’s conditions, enabling decisions that are fairer in practice. First, experiential conjoint analysis was used to obtain individual empirical utility functions for drinking mug designs. Each empirical utility function represented individual members who were part of a design team. Then, a number of functions for constructing group preference were analysed using both randomly generated preferences and empirical preferences derived from the experiential conjoint survey. The analysis involved checking each of Arrow’s conditions, as well as assessing the potential impact of strategic voting. Based on the results, methods that should be used to aggregate group preference within a design team in practice were identified and recommended.

  • View HTML
    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Impossible by design? Fairness, strategy, and Arrow’s impossibility theorem
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Impossible by design? Fairness, strategy, and Arrow’s impossibility theorem
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Impossible by design? Fairness, strategy, and Arrow’s impossibility theorem
      Available formats
      ×
Copyright
Distributed as Open Access under a CC-BY-NC-ND 4.0 license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Corresponding author
Email address for correspondence: cagan@cmu.edu
References
Hide All
Arrow, K. J. 1950 A difficulty in the concept of social welfare. The Journal of Political Economy 58 (4), 328346.
Austen-Smith, D. & Banks, J. S. 1996 Information aggregation, rationality, and the Condorcet jury theorem. The American Political Science Review 90 (1), 3445.
Bartholdi, J. J., Tovey, C. A. & Trick, M. A. 1989 The computational difficulty of manipulating an election. Social Choice and Welfare 6 (3), 227241.
Black, D. et al. 1958 The Theory of Committees and Elections. Springer.
Cagan, J. & Vogel, C. M. 2012 Creating Breakthrough Products: Innovation From Product Planning to Program Approval, 2nd edn. FT Press.
de Condorcet, N.1785, Essai sur l’application de l’analyse á la probabilité des décisions rendues á la pluralité des voix.
Dong, A., Hill, A. W. & Agogino, A. M. 2004 A document analysis method for characterizing design team performance. Journal of Mechanical Design 126 (3), 378385.
Dwarakanath, S. & Wallace, K. M. 1995 Decision-making in engineering design – observations from design experiments. Journal of Engineering Design 6 (3), 191206.
Dym, C. L., Wood, W. H. & Scott, M. J. 2002 Rank ordering engineering designs: pairwise comparison charts and Borda counts. Research in Engineering Design 13, 236242.
Franssen, M. 2005 Arrow’s theorem, multi-criteria decision problems and multi-attribute preferences in engineering design. Research in Engineering Design 16 (1–2), 4256.
Frey, D. D. et al. 2009 The Pugh controlled convergence method: model-based evaluation and implications for design theory. Research in Engineering Design 20 (1), 4158.
Frey, D. D. et al. 2010 Research in engineering design: the role of mathematical theory and empirical evidence. Research in Engineering Design 21 (3), 145151.
Fu, K., Cagan, J. & Kotovsky, K. 2010 Design team convergence: the influence of example solution quality. Journal of Mechanical Design 132 (11), 111005.
Gibbard, A. 1977 Manipulation of voting schemes: a general result. Econometrica 45 (3), 665681.
Goucher-Lambert, K. & Cagan, J. 2015 The impact of sustainability on consumer preference judgments of product attributes. Journal of Mechanical Design 137 (August), 81401-1–11.
Green, P. 1974 On the design of choice experiments involving multifactor alternatives. Journal of Consumer Resarch 1 (2), 6168.
Green, P. & Wind, Y. 1975 New way to measure consumers’ judgments. Harvard Business Review 53 (4), 107117.
Hazelrigg, G. A. 1996 The implications of Arrow’s impossiblity theorem on approaches to optimal engineering design. Journal of Mechanical Design 118 (2), 161164.
Hazelrigg, G. A. 1999 An axiomatic framework for engineering design. Journal of Mechanical Design 121 (3), 342.
Hazelrigg, G. A. 2010 The Pugh controlled convergence method: model-based evaluation and implications for design theory. Research in Engineering Design 21 (3), 143144.
Hoyle, C. & Chen, W. 2011 Understanding and modelling heterogeneity of human preferences for engineering design. Journal of Engineering Design 22 (8), 583601.
Jacobs, J. F., van de Poel, I. & Osseweijer, P. 2014 Clarifying the debate on selection methods for engineering: Arrow’s impossibility theorem, design performances, and information basis. Research in Engineering Design 25 (1), 310.
Janssen, O. 2000 Job demands, perceptions of effort–reward fariness and innovative work behaviour. Journal of Occupational and Organizational Psychology 73 (3), 287302.
Kaldate, A. et al. 2006 Engineering parameter selection for design optimization during preliminary design. Journal of Engineering Design 17 (March 2015), 291310.
Katsikopoulos, K. 2009 Coherence and correspondence in engineering design: informing the conversation and connecting with judgment and decision-making research. Judgment and Decision Making 4 (2), 147153.
Keeney, R. L. 2009 The foundations of collaborative group decisions. International Journal of Collaborative Engineering 1, 4.
Kelly, J. C. et al. 2011 Incorporating user shape preference in engineering design optimisation. Journal of Engineering Design 22 (9), 627650.
Kuhfeld, W. F.(2010) Marketing research methods in SAS. SAS Technical Papers, MR-2010.
Ladha, K., Miller, G. & Oppenheimer, J.2003 Information Aggregation by Majority rule: Theory and Experiment. http://www.gvptsites.umd.edu/oppenheimer/research/jury.pdf.
Li, H., Bingham, J. B. & Umphress, E. E. 2007 Fairness from the top? Perceived procedural justice and collaborative problem solving in new product development. Organization Science 18 (2), 200216.
Luce, R. D. & Raiffa, H. 1957 Games and Decisions. Courier Dover Publications.
Luce, R. D. & Tukey, J. W. 1964 Simultaneous conjoint measurement: a new type of fundamental measurement. Journal of Mathematical Psychology 1 (1), 127.
McComb, C., Goucher-Lambert, K. & Cagan, J. 2015 Fairness and manipulation: an empirical study of Arrow’s impossibility theorem. In International Conference on Engineering Design, Milan, Italy, pp. 267276.
Nisan, N.(Ed.) 2007 Algorithmic Game Theory. Cambridge University Press.
Nurmi, H. 2012 On the relevance of theoretical results to voting system choice. In Electoral Systems: Studies in Choice and Welfare (ed. Felsenthal, D. S. & Machover, M.), pp. 255274. Springer.
Olewnik, A. T. & Lewis, K. 2005 On validating engineering design decision support tools. Concurrent Engineering 13 (2), 111122.
Olewnik, A. T. & Lewis, K. 2008 Limitations of the House of Quality to provide quantitative design information. International Journal of Quality and Reliability Management 25 (2), 125146.
Orsborn, S., Cagan, J. & Boatwright, P. 2009 Quantifying aesthetic form preference in a utility function. Journal of Mechanical Design 131 (6), 61001-1–10.
Paulus, P. B., Dzindolet, M. T. & Kohn, N. 2011 Collaborative creativity, group creativity and team innovation. In Handbook of Organizational Creativity (ed. Mumford, M. D.), pp. 327357. Elsevier.
Pemmaraju, S. & Skiena, S. 2003 Computational Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Cambridge University Press.
Petiot, J.-F. & Grognet, S. 2006 Product design: a vectors field-based approach for preference modelling. Journal of Engineering Design 17 (3), 217233.
Reich, Y. 1994 Layered models of research methodologies. Artificial Intelligence for Engineering Design, Analysis and Manufacturing 8 (4), 263274.
Reich, Y. 2010 My method is better! Research in Engineering Design 21 (3), 137142.
Reid, T. N., Macdonald, E. F. & Du, P. 2013 Impact of product design representation on customer judgment. Journal of Mechanical Design 135 (9), 91008-1–12.
Saari, D. G. 2011 Geometry of Voting. Elsevier B.V.
Saari, D. G. & Sieberg, K. K. 2004 Are partwise comparisons reliable? Research in Engineering Design 15 (1), 6271.
Satterthwaite, M. A. 1975 Strategy-proofness and Arrow’s conditions: existence and correspondence theorems for voting procedures and social welfare functions. Journal of Economic Theory 10 (2), 187217.
Scott, M. J. & Antonsson, E. K. 1999 Arrow’s theorem and engineering design decision making. Research in Engineering Design 11, 218228.
See, T.-K. & Lewis, K. 2006 A formal approach to handling conflicts in multiattribute group decision making. Journal of Mechanical Design 128 (4), 678.
Seidenfeld, T., Kadane, J. B. & Schervish, M. J. 1989 On the shared preference of two Bayesian decision makers. The Journal of Philosophy 86 (5), 225244.
Sen, A. 1977 Social choice theory? A re-examination. Econometrica 45 (1), 5388.
Sylcott, B., Cagan, J. & Tabibnia, G. 2013 Understanding consumer tradeoffs between form and function through metaconjoint and cognitive neuroscience analyses. Journal of Mechanical Design 135 (10), 101002-1–13.
Tovares, N., Cagan, J. & Boatwright, P. 2014 Experiential conjoint analysis: an experience-based method for eliciting, capturing, and modeling consumer preference. Journal of Mechanical Design 36 (10), 101404-1–12.
Train, K. 2003 Discrete Choice Methods With Simulation. Cambridge University Press.
Wegner, D. M. 1987 Transactive memory: a contemporary analysis of the group mind. In Theories of Group Behavior, pp. 185208. Springer.
Weingart, L. R. et al. 2005 Functional diversity and conflict in cross-functional product development teams: considering representational gaps and task characteristics. In Understanding Teams (ed. Neider, L. L. & Schriesheim, C. A.), pp. 89110. Information Age Publishing.
Yeo, S. H., Mak, M. W. & Balon, S. a. P. 2004 Analysis of decision-making methodologies for desirability score of conceptual design. Journal of Engineering Design 15 (2), 195208.
Young, H. P. 1995 Equity: In Theory and Practice. Princeton University Press.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Design Science
  • ISSN: -
  • EISSN: 2053-4701
  • URL: /core/journals/design-science
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed