David A. Kenny
March 23, 2021

The perception that A has of B's perception of C or A(B(C)) is a triadic perception. Person A is called the judge, person B the perceiver, and person C the target. In one study, we asked judges to estimate how much the characters of television show like one another. So we asked a University of Connecticut undergraduate (judge) how much Carla (perceiver) liked Cliff (target). There are some important special cases of triadic perceptions:
• A(B(A)): dyadic meta-perceptions (see meta-accuracy)
• A(B(B)): judgment of how a person sees self
• A(A(B)): how A thinks that A views B; normally the same as A(B)
• A(A(A)): how A thinks that A views A; normally the same as A(A) or self perception
One important use of triadic ratings is in families. We can ask mothers how they think their son relates to the father or M(S(F)). Note that triadic meta-accuracy can be defined as M(S(F)) = S(F).

There are seven sources of variance in triadic ratings:

Individual
judge: a judge's general view of how people see others
perceiver: how people think a person tends to see others
target: how people think a person is seen by others

judge by perceiver: disagreements between judges in how a person sees others
judge by target: disagreements between judges in how a person is seen by others
perceiver by target: agreement between judges in how a person uniquely views a target

judge by perceiver by target: most of this is likely error

There are 16 univariate correlations:

Individual

• judge with perceiver (or i with j)
• judge with target (or i with k)
• perceiver with target (or j with k)

• JP with PJ (or ij with ji)
• JT with TJ (or ik with ki)
• PT with TP (or jk with kj)
• JP with JT (or ij with jk)
• JP with TJ (or ij with kj)
• JT with PT (or jk with ik)
• JP with TJ (or ij with kj)
• JP with JT (or ij with ik)
• JT with TP (or ik with kj)

• ijk with ikj
• ijk with jik
• ijk with kji
• ijk with jki or kij

The are so many bivariate correlations that they are too numerous to describe. In general, each a variable can be correlated with all other components at that level. So individual effects are correlated with individual effects, dyadic with dyadic, and triadic with triadic.

Most of the work that I have done on triadic analyses of perception has been with Charles Bond. Many of the insights and almost all of the math are due to him.

Bond, C. F., Jr., Horn, E. M., & Kenny, D. A. (1997). A model for triadic relations. Psychological Methods, 2, 79-94. doi:10.1037/1082-989X.2.1.79
Kenny, D. A., Bond, C. F., Jr., Mohr, C. D., & Horn, E. M.(1996). Do we know how much people like one another? Journal of Personality and Social Psychology, 71, 928-936. doi:10.1037/0022-3514.71.5.928

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