Donald G. SaariInstitute for Mathematical Behavioral Sciences

University of California, Irvinedsaari@uci.edu

http://www.imbs.uci.edu

The responsibility of the social sciences to assist the engineering and physical

sciences

1. Data 2. Decisions

3. Multi-scale analysis4. 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

7 58 9 4

6

Nonparametric statistics

A B C 23 21 1924 25 2018 17 22

Subjective

A B C

123

Kruskal Wallis 17 15 13So, A>B>C

Other methods: A>B>CA>B>C

A>C>B

Deanna HaunspergerJASA 1992

Here, data defines a profile with 27 “voters”;

vote with some positional method

E.g., K-W is the Borda method

ranks

So, she couldtransfer results

from voting to statistics

Voting results 5 ABCD 9 BDAC7 ACBD 8 CBAD9 ADBC 11 CDAB4 BACD 8 DBAC7 BCAD 10 DCAB

Plurality ranking: A>B>C>D with 21:20:19:18 talliesDrop any alternative, and outcome flips to reflect D>C>B>A

Drop any two alternative, and outcome flips to reflect A>B>C>DMy dictionary results:

for any number of candidates specify any ranking for each subset of candidatesspecify a positional voting rule for each subset of candidates

In almost all cases, an example can be created!Main exception, Borda Count!

Using my dictionary of voting outcomes,Haunsperger characterized the outcome of all of

these non-parametric rulesExample:

The Kruskal-Wallis Test is bad, very badOf 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

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

Choice of non-parametric rule no longer is “subjective!”

Decisions: often by parts

Already know that information is lost when using “parts,”

and it occurs in engineering, etc.

criteria become “voters”Social choice, voting theory shows why “bad

decisions” can easily be made

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.

Nano systems

?

New questions,New relationshipsPart with the parts

Newton’s Headache

Where can we find

structure, a simpler

multiscale system to analyze?

Multi-scale analysisSociology, health policy, etc.

• 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?

Sen’s TheoremConflict: Individual rights vs societal welfare

Note: Emphasis is on Pairwise decisions!Lost information

{A,B} {B, C} {A, C}

1 A>B>C2 B>C>A

1 AB BC -- 2 -- BC CA

AB BC CACycle!!

Shirt

Multi-scale analysis

Micro Macro

What can go right, what can go wrong?One example: Path dependencyRather 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

Many things can go wrong!

Path dependency - simple example

10 A>B>C>D>E>F10 B>C>D>E>F>A10 C>D>E>F>A>B

D

E C B

A F

DC

BA

F

Everyone prefers C>D>E>FNot apparent

Physics? Chemistry? ElectronicsCalculus; line integrals

from here

to herecan depend on path

Pairwise comparisons?Depending on the path optimal decisions are made, anything

can be selected!To select F:

Unanimous or two-thirds support: Very strong “evidence” that F is “optimal”

“Severing effect”

• 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?

Sen

Macro

Compatibility conditionsAll elements are needed

some combinations are not compatible

compensative

Add natural conditions on rule; e.g., maybe some macro

effects determined by one force

unanimity type conditionsResult: 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 wrongPositive results are being

developed

Creating all possible Sen examples

1: CEDAB; 2: BCEDA

Individual rights; or imposing on othersDysfunctional

society?

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 EA2 AB BC CD DA CE EA

Outcome AB BC CD DA CE EA

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).

Similar kinds of effects for multi-

scale analysis

Strong negative externality For everyone over each cycle!

Over the last week, we have explored a small but important part of “the incredible complexity of

the social sciences” and, in particular, economicsA 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 settingA 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 areasA 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!