On the Measurement of Interpersonal Trust Transfer: Proposal of Indexes

Abstract

This paper investigates the measurement of trust transfer in interpersonal contexts. Despite the importance of this topic, little evidence of comparable indicators exists to fill the current gap in knowledge regarding the measurement of interpersonal transference of trust and its reciprocal. We propose a modification of the classical structure of a widely accepted experimental setting for analyzing trust (i.e. a trust game) and build two indexes for the measurement of trust transfer and its reciprocation. Several properties of these indicators are investigated to examine their robustness and accuracy for measuring the transference of interpersonal trust. Furthermore, using data from our own modified trust game, we provide an empirical examination of both indexes. The results show that the existence of a mutually known third party fosters a stronger willingness to achieve cooperative behavior in an anonymous trust game; thus, the transference of interpersonal trust works in both directions of the dyad.

Appendix: The process of building the trust transfer reciprocation index

We establish the following notation:

• $y_{2}^{j}$: trust received by the β-type k(j)-trustee from the j-trustor

• $y_{12}^{j}$: trust placed by the j-trustor to the β-type k(j)-trustee

• $y_{21}^{j}$: trust returned by the β-type k(j)-trustee to the j-trustor

We specify that trust transfer reciprocity is maximized in a given period when a trustor and a β-type trustee trust one another in the same proportion of total trust that each has in that period.

Because the initial endowment of the trustor in our trust game is M _j , the proportion of trust placed by the j-trustor in the β-type k(j)-trustee is $\frac{{y_{12}^{j} }}{{M_{j} }}$.

Moreover, because the trust received by the β-type k(j)-trustee is $y_{2}^{j} = my_{12}^{j}$, the proportion of trust returned to the j-trustor to the β-type k(j)-trustee is: $\frac{{y_{21}^{j} }}{{my_{12}^{j} }}$.

According to our definition of trust transfer reciprocation, both proportions must be (at least) equal for trust transfer reciprocation to be maximized. Therefore, $\frac{{y_{12}^{j} }}{{M_{j} }} = \frac{{y_{21}^{j} }}{{my_{12}^{j} }}$ if and only if $\frac{{M_{j} y_{21}^{j} }}{{m\left( {y_{12}^{j} } \right)^{2} }} = 1$.

Henceforth, we obtain the following expression:

$$ TTR_{21}^{j} = \left\{ {\begin{array}{*{20}c} {\frac{{M_{j} y_{21}^{j} }}{{m\left( {y_{12}^{j} } \right)^{2} }}} & {y_{12}^{j} \ne 0} \\ 0 & {y_{12}^{j} = 0} \\ \end{array} } \right.. $$

Nonetheless, this index is not bounded within the interval $\left[ {0,1} \right]$.¹ To solve this equation, we propose the following expression:

$$ TTR_{21}^{j} = \min \left\{ {\frac{{M_{j} y_{21}^{j} }}{{m\left( {y_{12}^{j} } \right)^{2} }},1} \right\}. $$

Furthermore, the above expression is an undefined problem if the denominator is zero. Because the multiplier must reflect a return on an investment and is, by definition, positive, the denominator of the above expression reaches zero if and only if the trust placed by the j-trustor in the β-type k(j)-trustee is zero (i.e. $y_{12}^{j} = 0$). Hence, to avoid such a possibility, we make the following adjustment:

$TTR_{21}^{j} = \min \left\{ {\frac{{M_{j} y_{21}^{j} }}{{\max \left\{ {m\left( {y_{12}^{j} } \right)^{2} ,1} \right\}}},1} \right\}$.

$$ \square $$