### Abstract

The purpose of this paper is to deduce axiomatically a bilateral evaluation function that has various meanings on caring about the other e.g. equalitarian, maximin, competition etc. The evaluation function of one's and the other's payoffs looks like a little complicated including absolute value, but the function can be deduced from very simple axioms. Concretely speaking, the axioms are (1) comparable payoffs between actors and (2) positive affine transformation constancy on payoffs and evaluations respectively. These two axioms look like not including equality, but the evaluation function from the axioms includes equality. Because increasing affine transformation keeps the order property of payoffs. By the way the equality is defined as-|x-y| where x is one's payoff and y is the other's payoff. Then the asymmetric property of absolute value of equality originates from the asymmetric property of the order of payoffs.

Original language | English |
---|---|

Pages (from-to) | 301-316 |

Number of pages | 16 |

Journal | Sociological Theory and Methods |

Volume | 24 |

Issue number | 2 |

Publication status | Published - 2009 |

### Fingerprint

### Keywords

- Caring
- Increasing affine transformation
- Interpersonal payoff comparison

### ASJC Scopus subject areas

- Social Sciences (miscellaneous)
- Sociology and Political Science

### Cite this

**An axiomatic system of social motivations in dyadic relation : Potential existence of altruism and egalitarianism.** / Muto, Masayoshi.

Research output: Contribution to journal › Article

*Sociological Theory and Methods*, vol. 24, no. 2, pp. 301-316.

}

TY - JOUR

T1 - An axiomatic system of social motivations in dyadic relation

T2 - Potential existence of altruism and egalitarianism

AU - Muto, Masayoshi

PY - 2009

Y1 - 2009

N2 - The purpose of this paper is to deduce axiomatically a bilateral evaluation function that has various meanings on caring about the other e.g. equalitarian, maximin, competition etc. The evaluation function of one's and the other's payoffs looks like a little complicated including absolute value, but the function can be deduced from very simple axioms. Concretely speaking, the axioms are (1) comparable payoffs between actors and (2) positive affine transformation constancy on payoffs and evaluations respectively. These two axioms look like not including equality, but the evaluation function from the axioms includes equality. Because increasing affine transformation keeps the order property of payoffs. By the way the equality is defined as-|x-y| where x is one's payoff and y is the other's payoff. Then the asymmetric property of absolute value of equality originates from the asymmetric property of the order of payoffs.

AB - The purpose of this paper is to deduce axiomatically a bilateral evaluation function that has various meanings on caring about the other e.g. equalitarian, maximin, competition etc. The evaluation function of one's and the other's payoffs looks like a little complicated including absolute value, but the function can be deduced from very simple axioms. Concretely speaking, the axioms are (1) comparable payoffs between actors and (2) positive affine transformation constancy on payoffs and evaluations respectively. These two axioms look like not including equality, but the evaluation function from the axioms includes equality. Because increasing affine transformation keeps the order property of payoffs. By the way the equality is defined as-|x-y| where x is one's payoff and y is the other's payoff. Then the asymmetric property of absolute value of equality originates from the asymmetric property of the order of payoffs.

KW - Caring

KW - Increasing affine transformation

KW - Interpersonal payoff comparison

UR - http://www.scopus.com/inward/record.url?scp=74549217831&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=74549217831&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:74549217831

VL - 24

SP - 301

EP - 316

JO - Sociological Theory and Methods

JF - Sociological Theory and Methods

SN - 0913-1442

IS - 2

ER -