Donald G. Saari Institute for Mathematical Behavioral Sciences University of California, Irvine dsaari@uci.edu http://ww

1. The responsibility of the social sciences to assist the engineering and physical sciences Donald G. Saari Institute for Mathematical Behavioral Sciences University of California, Irvine dsaari@uci.edu http://www.imbs.uci.edu 1. Data 2. Decisions 3. Multi-scale analysis 4. Allocations -- space Commonality: Aggregation and allocation rules The bread and butter of social sciences Plan: take representative issues and show how ideas from social choice and social science give value added Christian Klamler and Ulrich Pferschy

2. 7 5 8 9 A B C A B C ranks 4 6 23 21 19 24 25 20 18 17 22 Nonparametric statistics Subjective Deanna Haunsperger JASA 1992 3 2 1 E.g., K-W is the Borda method Kruskal Wallis 17 15 13 So, A>B>C So, she could transfer results from voting to statistics Other methods: A>B>C A>C>B A>B>C Here, data defines a profile with 27 “voters”; vote with some positional method

3. Voting results 5 ABCD 9 BDAC 7 ACBD 8 CBAD 9 ADBC 11 CDAB 4 BACD 8 DBAC 7 BCAD 10 DCAB Plurality ranking: A>B>C>D with 21:20:19:18 tallies Drop any alternative, and outcome flips to reflect D>C>B>A Drop any two alternative, and outcome flips to reflect A>B>C>D My dictionary results: for any number of candidates specify any ranking for each subset of candidates specify a positional voting rule for each subset of candidates In almost all cases, an example can be created! Main exception, Borda Count!

4. Using my dictionary of voting outcomes, Haunsperger characterized the outcome of all of these non-parametric rules Example: The Kruskal-Wallis Test is bad, very bad Of all possible non-parametric methods, the KW is by far the best! With Anna Bargagliotti, using my approach toward voting theory to understand and characterize all consequences of all non-parametric methods Choice of non-parametric rule no longer is “subjective!” Power indices: OR, cost allocation, etc. v(S+i) - v(S) pi = Σ λS(v(S+i) - v(S)) A. Laruelle and V. Merlin -- used my dictionary, found Shapley value is identified with Borda Count D. Saari and K. Sieberg

5. Decisions: often by parts criteria become “voters” Social choice, voting theory shows why “bad decisions” can easily be made Already know that information is lost when using “parts,” and it occurs in engineering, etc.

6. ? Nano systems Multi-scale analysis New questions, New relationships Part with the parts Sociology, health policy, etc. Newton’s Headache Where can we find structure, a simpler multiscale system to analyze? Biological systems have the first level of organization at the nanoscale. Proteins, DNA, RNA, ion channels are nanoscale systems that leverage molecular interactions to perform specific tasks. Integrated nano-bio systems have emerged as strong candidates for single molecule detection, genomic sequencing, and the harnessing of naturally occurring biomotors. Design of integrated nano-bio devices can benefit from simulation, just as the design of microfluidic devices have benefited. Currently a large stumbling block is the lack of simulation methods capable of handling nanoscale physics, device level physics, and the coupling of the two.

7. Lost information Sen’s Theorem Shirt Conflict: Individual rights vs societal welfare Note: Emphasis is on Pairwise decisions! • Inputs: Preferences are transitive, no restriction • Outputs: No societal cycles • Procedure:Pareto • Minimal Liberalism: At least each of two agents are decisive, each over assigned pairs • Conclusion: No procedure exists • Why? What causes this theorem? 1 A>B>C 2 B>C>A {A,B} {B, C} {A, C} 1 AB BC -- 2 -- BC CA AB BC CA Cycle!!

8. Macro Micro Multi-scale analysis What can go right, what can go wrong? Many things can go wrong! One example: Path dependency Rather than optimality, or establishing connections between scales, it is possible for the outcome to reflect the order in which elements are analyzed rather than the micro behavior

9. from here to here Path dependency - simple example 10 A>B>C>D>E>F 10 B>C>D>E>F>A 10 C>D>E>F>A>B Everyone prefers C>D>E>F Pairwise comparisons? Not apparent “Severing effect” Depending on the path optimal decisions are made, anything can be selected! To select F: Physics? Chemistry? Electronics D E C B A F D Calculus; line integrals C B A F Unanimous or two-thirds support: Very strong “evidence” that F is “optimal” can depend on path

10. Sen Macro • Inputs: Preferences are transitive, no restriction • Outputs: No societal cycles • Procedure:Pareto • Minimal Liberalism: At least each of two agents are decisive, each over assigned pairs • Conclusion: No procedure exists • Why? What causes this theorem? Add natural conditions on rule; e.g., maybe some macro effects determined by one force unanimity type conditions Result: A Sen-type conclusion; Impossibility Message:Beware; evidence may appear to provide overwhelming support about the existence of a connection, a result, etc., yet it can be wrong Positive results are being developed Compatibility conditions All elements are needed some combinations are not compatible compensative

11. Creating all possible Sen examples 1. Start with desired societal outcome; e.g, AB, BC, CD, DA and BC, CE, EA, AB. Assign to each agent. 1 AB BC CD DA CE EA 2 AB BC CD DA CE EA Outcome AB BC CD DA CE EA Strong negative externality For everyone over each cycle! 1: CEDAB; 2: BCEDA 2. For each cycle and each agent, assign another agent to be decisive over a pair; e.g., AB to 1, and BC to 2 3. Now find associated transitive preferences for agents (here, just reverse blocked off pairwise ranking). Individual rights; or imposing on others Dysfunctional society? Similar kinds of effects for multi-scale analysis

12. Over the last week, we have explored a small but important part of “the incredible complexity of the social sciences” and, in particular, economics A lesson learned is that guidance, direction, and possible resolutions for these many areas come from examining what happens in the “simpler” social choice or voting setting A lesson learned is that the same concepts extend to almost all science areas. These are very important issues; join in the analysis of them, particularly the extension of social choice to other areas A lesson Lillian and I learned is the beauty of this area, the incredible hospitality of all, starting with Christian2 and extends and includes so many others! Our thanks to all for a most memorable visit!