Dynamics of Negative Evaluations in the Information Exchange of Interactive Decision-Making Teams: Advancing the Design of Technology-Augmented GDSS

Abstract

Applications of technology that contribute to managing decision-making teams for their objectives benefit from an explicit account of microprocessing in the information exchange of team members. While negative evaluations are well recognized as a key information type in this exchange, the micro-processing that underlies its exchange has not been well defined. Negative evaluations will be proposed to differ from other information types because of their dual properties as information and affect. We propose dynamics that are implied by the duality in negative evaluations we cite and report empirical studies that test abstract generalizations on the proposed dynamics. We then give an explicit form to exchange of negative evaluations in a numerical model of information exchange and use the model in exercises that directly demonstrate the proposed properties of negative evaluations in information exchange. Finally, we review contributions that the discourse offers to the design of AI-supported GDSSs for managerial objectives in the exchange of information in ill-structured decision making and introduce architecture of a prototype GDSS that implements quality-maximizing information exchange. Directions for subsequent study are discussed.

Appendix

1.1 Numerical Model of Dynamic Information Exchange in Interactive Groups and Teams

1.1.1 Idea Generation

Eq (1) and (2) are forms for the initiation of single source and multi-source ideas, respectively.

$$ {J}_J^{(1)}={K}_{a,j}\ \left({A}_j-{\alpha}_j\left(\ {J}_1^{(1)},\dots .,{J}_n^{(1)}\right)\right),{J}_i^{(1)}=0 $$

(1)

$$ {J}_j^{(2)}={K}_{a,j}\ \left({\sum}_{j\ne k}{J}_K^{(1)}\right)\left({A}_j-\alpha \left({J}_1^{(1)},\dots .,{J}_n^{(1)}\right)\ \right)+{K}_{b,j}\left[{\left({\sum}_K{J}_K^{(1)}\right)}^2-\left({c}_1{\sum}_k{J}_K^{(2)}\right)\right],{J}_j^{(2)}(0)=0 $$

(2)

J_j⁽¹⁾ is the number of single source ideas that the j^th member initiates in a defined time interval.

J_j⁽²⁾ is the number of multi-source rate ideas the j^th member initiates in a defined time interval.

A_j is the initial pool of ideas of the j^th member.

${a}_j\left({J}_1^{(1)}\right),\dots {J}_n^{(1)}$ is the proportion of ideas in the j^th members pool that already have been given in the group. K is a mediator of the initiation of “realized” ideas. This rate is conceptualized as trust by members on equity in information exchange, i.e. that evaluations will be meritoriously distributed. Eqs. (7) and (8) give a form to this dependency.

Single Source Ideas. In eq. (1), the rate of initiating single source ideas, ${J}_J^{(1)}$ is considered to be a function of this member’s initial idea “pool” (A_j) as corrected by the number of ideas already given by this member and all other team members or ideas that are common to their idea pools.

Multiple Source Ideas. One of the contributions of interactive groups and teams is in the capability of members to generate ideas that combine ideas of other members. This is given a form in (2) for J_j⁽²⁾. The first term on the RHS of J_j⁽²⁾ results from the combination of all single source ideas given by team members other than j and the sum of the j^th member’s unduplicated ideas (either already initiated or in his or her initial idea pool). The second term is defined as the number of unique combinatorial ideas by all individual members of the team from their own ideas. The third term removes all combinatorial ideas already given by any team member.

1.1.2 Dynamics of Evaluations

The form given dynamic evaluations follows from conjecture that initial rates are decreasing with increases in the variance in the status distribution ${\sum}^{\Delta _{jk}}$ and asymptotic rates will be increasing. A defensible assumption on the frequency of positive and negative evaluations is that b_nP_kj < c_nN_kj for feasible ranges of b_n and c_n

$$ {N}_{jk}=\left( 1/{\varDelta}_{kj}\right)\left({a}_n{K}_j\hbox{--} {b}_n{P}_{kj}+{c}_n{N}_{kj}+{d}_n\right)\mid {N}_{jk}(0)= 1//{\varDelta}_{kj}{d}_n $$

(3)

$$ {P}_{jk}=\left({\varDelta}_{kj}\right)\left({a}_n{K}_j+{b}_n{P}_{kj}-{c}_n{N}_{kj}+{d}_n\right);{P}_{jk}(0)={\varDelta}_{kj}.{d}_p $$

(4)

Where N, P and J are as previously defined and b_n, c_n and d_n are rate parameters for returning negative evaluations for the receipt of the respective information types. The Δ function for effects of jk status differences will be defined below.

1.1.3 Bias in Microlevel Status Judgments: Defining the Δ Function

Contrary to expected value formulations in which gains and losses are treated equivalently, team members are generally considered to be loss aversive. That is, they will generally “pay” more to avoid a loss with a given likelihood than to receive a gain of the same likelihood. In the case of status judgments, this can be interpreted as meaning that they will overweight the possible status loss from a negative evaluation by a higher status team member in comparison to a negative evaluation from a team member who is lower in status by an equivalent distance. This bias is considered to be a common consequence of unequal status in a group or team and is given a candidate form in eq. (5)

$$ {\displaystyle \begin{array}{c}\Delta jk\kern0.75em =1+\left(\upsigma \mathrm{j}-\upsigma \mathrm{k}\right)\upalpha 1/\left(2\mathrm{n}+1\right)\kern1.5em If\kern0.5em \upsigma \mathrm{j}\ge \upsigma \mathrm{k}\\ {}=1+\left(\upsigma \mathrm{j}-\upsigma \mathrm{k}\right)\upalpha 2/\left(2\mathrm{n}+1\right)\kern1.5em If\kern0.5em \upsigma \mathrm{j}<\upsigma \mathrm{k}\\ {}1<\upalpha 2<\upalpha 1<2\mathrm{n}+1\end{array}} $$

(5)

Where Δ_jk is the judged distance between the j^th and k^th member.

σ_j, σ_jk are the actual status of these members, α₁ and α₂ are parameters, and n is team size.

Dynamics of Member Status.

Member status in an interactive team depends on both an initial set of m attributes (e.g., organizational position, education, and age) and the evaluations that are received over the course of the team’s interaction. A form for initial status and its dynamic variation through information exchange can be written as follows as eq. (6).

$$ {\sigma}_j={\alpha}_s\sum \limits_{j\ne k}{\Delta}_{kj}\ {P}_{kj}-{\beta}_s\sum \limits_{j\ne k}{\Delta }_{kj}{N}_{j,k},{\sigma}_j(0)=\frac{\sum_i{m}_j^{(i)}{w}^{(i)}}{\sum_k{\sum}_i{m}_j^{(i)}{w}^{(i)}} $$

(6)

σ is the member’s status in a time interval.

a_{s and} β_s are effects of receipts of positive and negative evaluations, respectively, as weighted by the status distance between k and j. The Δ function adjusts the magnitude of effects differentially for ${\dot{\sigma}}_j\ge {\dot{\sigma}}_k$ and ${\dot{\sigma}}_k\ge {\dot{\sigma}}_j$.

m⁽ⁱ⁾,i = 1, n are a set of socio-demographic variables that are relevant to status judgments.

w⁽ⁱ⁾,i = 1,n are the weights of these variables in status judgments.

Δ, P and N are as previously defined.

A defensible assumption on parameters in eq. (6) that follows from Assumptions 1 and 2 and link changes of a member’s status to the receipt of evaluations in the team’s information exchange is that β_s ≫ a_s, i.e., the receipt of negative evaluation has a significantly greater effect on member status than the receipt of a positive evaluation.

1.1.4 Equity and Trust in the Rate Mediator

The extent to which a team member will be willing to initiate message types with higher social risk depends in part on their trust in other team members to interact “equitably” in information exchange. Equitably here means to distribute negative evaluations on the basis of the number of ideas initiated rather than a member’s status in the team. Trust has now been shown to be an important mediator of team performance across applications (e.g. Jarvenpaa et al. 2004; Lewis and Weigert 2012).

Trust is an argument of K in eqs. (1) and (2) and depends on perceived equity. Equity in information exchange is defined here in terms of a distribution of positive and negative evaluations to members that is proportional to the ideas they initiate in information exchange. This is counter to the tendency to under-evaluate higher status members and over-evaluate lower status members that is frequently observed in teams. Similar biases have been demonstrated in non-linear differences in the weight given likely and unlikely events in decision making (e.g. Ansel et al. 2016). The generation of trust in the information exchange of teams can, in turn, be conceptualized in terms of deviations from an equity state as in eq. (8) where inequity (E) is defined as eq. (7). It can further be assumed that inequity in the distribution of negative evaluations is weighted more heavily by team members than inequity in the distribution of positive evaluation.

$$ {E}_j={c}_{n1}\left[\frac{J_j}{\sum_k{J}_k}-\frac{\sum_k{\Delta }_{jk}{a}_{n2}{N}_{jk}}{\sum_k{\sum}_l{\Delta }_{kl}{a}_{n2}{N}_{kl}}\right]+{c}_{p1}\left[\frac{J_j}{\sum_k{J}_k}-\frac{\sum_k{\Delta }_{jk}{a}_{p2}{N}_{jk}}{\sum_k{\sum}_l{\Delta }_{kl}{a}_{p2}{N}_{kl}}\right],{c}_{n1}\gg {c}_{p1} $$

(7)

$$ {T}_j={\left[1+{E}_j\right]}^{-1},{T}_j\in \left(0,1\right) $$

(8)

T_j is an index of the level of trust in the j^th member, T∈(0,1).

E_j is the j^th member’s judgment of inequity in the group. E = 0 indicates perfect equity i.e. the absence of inequity.

J_j is total ideas (J⁽¹⁾ + J⁽²⁾).

N_jk is the number of negative evaluations the j^th member receives from the k^th member a time.

interval.

P is the number of positive evaluations the j^th member receives from the k^th member in a time.

interval.

∆_jk is the difference in status between the j^th and k^th member (∆_k − ∆_j).

a_n2, a_p2i, c_n, c_p are rate constants

1.1.5 A Quality Function for an Ill-Structured Decision

The forgoing account of information processing hypothesizes that the quality of an ill-structured decision (Q_L) will be (1) increasing in idea numbers and (2) decreasing when the ratio of negative evaluations is not in a bounded interval and (3) decreasing when negative evaluations are not sent to members in proportional to their idea initiation. This is given a form in eq. (9).

$$ {Q}_L={\sum}_j{J}_j^i-\left|{\sum}_j{J}_j-r{\sum}_{k\ne j}{N}_{kj}\right|-{\sum}_j{\left[\frac{J_j}{\sum_k{J}_k}-\frac{\sum_{k\ne j}{N}_{jk}}{\sum_k{\sum}_{k\ne j}{N}_{jk}}\right]}^2,t\in \Big(0,{t}_{m\Big)} $$

(9)

where J and N are as previously defined. The coefficient r is a proportionally constant that defines the number of negative evaluations relative to an idea that maximizes a quality objective.