The editor-manuscript game

Abstract

Scientific journals receive an increasing number of submissions and many of them will be desk rejected without receiving detailed feedback from reviewers. In fact, the number of desk rejections has risen dramatically in the last decade. In this paper, we contribute to the literature by examining an editor’s incentives either to issue a desk decision that is based solely on their imperfect private information about the manuscript’s quality or to send the paper to external peer reviewers that better reveal its quality. In our model, without external review, the journal editor receives an informative but imperfect signal of the manuscript’s quality. We focus on the case in which editors may differ in their decision accuracy, and highlight the consideration that even an editor with the best expertise and the best intentions may be unable to reach a perfect assessment of the manuscript’s quality. In our baseline model, the journal editor is not driven by financial interests but is nevertheless impurely altruistic in that the editor has a reputation consideration that may be tied to authors’ observational learning of the editor’s decision pathway (i.e., the process to reach the eventual editorial decision, which may or may not involve external peer review). Also, the editor in our setting is imperfectly informed about the manuscript’s quality unless they send the manuscript out to review. Our paper shows that high-ability editors tend to send fewer papers to external review than they should as a way to signal their ability. This is so because external peer review and editor’s decision expertise may substitute for each other.

Appendices

Appendix

Appendix A: Definitions for the benchmark scenario: the full-information case in which the editor’s type is common knowledge

Firstly, we consider the case in which the type-e editor receives a private signal $s_e = 0$, for $e = h, l$. In this setting, the editor compares the journal’s utility from three possible manuscript-decision pathways, that is, (1) $t = 0, a = 1$, (2) $t = 1$, and (3) $t = 0, a = 0$, before issuing their editorial decision. The journal’s utility for the three possible manuscript-decision pathways is as follows:

$$\begin{aligned}&U(\alpha | s_e=0) \nonumber \\&\quad = \left\{ \begin{array}{ll} b_e (\alpha | s_e) \cdot B + (1-b_e (\alpha | s_e)) \cdot (-d) &{} \text{ if } t = 0, a = 1 \\ b_e (\alpha | s_e) \cdot B -c &{} \text{ if } t = 1 \\ b_e (\alpha | s_e) \cdot (-D) &{} \text{ if } t = 0, a = 0 \end{array} \right\} \end{aligned}$$

(6)

where $b_e (\alpha | s_e)$ is the type-e editor’s belief that the manuscript’s quality is acceptable ($\theta = 1$), given the editor’s private signal $s_e$.

Following Dai and Singh (2020), a comparison of the journal’s expected utility corresponding to the three possible manuscript decision pathways reveals:

• (i) the editor does not send the paper to external peer reviewers and issues a desk-accept ($t = 0$ and $a = 1$) if $\alpha > {\overline{\alpha }}^e_{0}$, where ${\overline{\alpha }}^e_{0} = \frac{\rho _e(d-c)}{\rho _e(d-c) + (1-\rho _e) c},$

• (ii) they do not send the paper to external reviewers and issues a desk-reject ($t = 0$ and $a = 0$) if $\alpha \le {\underline{\alpha }}^e_{0}$, where ${\underline{\alpha }}^e_{0} = \frac{\rho _e c}{\rho _e c + (1-\rho _e)(B +D - c)}$, and

• (iii) if neither of the above then the editor sends the manuscript out to external review ($t = 1$).

The proof for the case in which the editor receives a positive private signal $s_e = 1$ proceeds in the same manner. The corresponding thresholds are ${\overline{\alpha }}^e_{1} = \frac{(1-\rho _e)(d-c)}{(1-\rho _e)(d-c) + \rho _e c}$ and ${\underline{\alpha }}^e_{1} = \frac{(1-\rho _e)c}{(1-\rho _e)c + \rho _e (B +D - c)}$.

Appendix B: Definitions for a real-life scenario

We define an upper bound ${\overline{B}}$ (derived in Dai and Singh 2020), beyond which the separating equilibrium would not exist, as

$$\begin{aligned} {\overline{B}} = \left( \frac{\rho _h}{1-\rho _h} \right) ^2 \cdot \frac{(rw +c)^2}{d-rw-c} + rw +c-D \end{aligned}$$

where $w=(1-\phi )/\phi$ is the relative weight the editor puts on their own reputational payoff compared to the journal’s utility, with $\phi \in [0,1]$.

A lower bound ${\underline{B}}$ (also derived in Dai and Singh 2020), exists such that if $B < {\underline{B}}$, the low-ability editor’s expected payoff from sending the paper to external peer reviewers would be so low that they would not have the incentive to send the manuscript out to external review, seen as:

$$\begin{aligned} {\underline{B}} = \left( \frac{\rho _l}{1-\rho _l} \right) ^2 \cdot \frac{(rw +c)^2}{d-rw-c} + rw +c-D. \end{aligned}$$

A unique separating equilibrium exists if and only if $\alpha \in [{\underline{\alpha }},{\overline{\alpha }}]$ where

$$\begin{aligned} {\underline{\alpha }} = \left\{ \begin{array}{ll} \frac{\rho _l(rw+c)}{\rho _l(rw+c) + (1- \rho _l)(B + D - rw -c)} &{} \text{ if } {\underline{B}} \le B \le \hat{B} \\ \frac{(1-\rho _h)(d-rw-c)}{\rho _h(rw+c) + (1- \rho _h)(d - rw -c)} &{} \text{ if } \hat{B} < B \le {\overline{B}} \end{array} \right\} \end{aligned}$$

and

$$\begin{aligned}{\overline{\alpha }} = \left\{ \begin{array}{ll} \frac{(1-\rho _l)(d-rw-c)}{\rho _l(rw+c) + (1- \rho _l)(d - rw -c)} &{} \text{ if } {\underline{B}} \le B \le \hat{B} \\ \frac{\rho _h(rw+c)}{\rho _h(rw+c) + (1- \rho _h)(B + D - rw -c)} &{} \text{ if } \hat{B} < B \le {\overline{B}} \end{array} \right\} \end{aligned}$$

with

$$\begin{aligned} \hat{B} = \frac{\rho _h \rho _l}{(1-\rho _h)(1-\rho _l)} \cdot \frac{(rw +c)^2}{d-rw-c} + rw +c-D. \end{aligned}$$

The proof for this result is similar to that of Proposition 3 in Dai and Singh (2020) and therefore we will skip it for the sake of brevity.

Appendix C: Could a peer-reviewed journal receive an even lower expected utility from assigning a high-ability journal editor as opposed to a low-ability one?

Following Dai and Singh (2020), we compare the journal’s expected utility from assigning each type of editor in the separating equilibrium (i.e., either a high-ability editor who does not send the paper to external peer reviewers and issues a desk-decision consistent with their private signal, or a low-ability editor who sends the manuscript out to external review regardless of their private signal). We have derived the journal’s expected utility in Sect. 2.

Consider an academic journal in which the manuscript decision is issued by a low-ability editor. In this case, the editor sends the manuscript out to external review. If the manuscript’s quality is acceptable ($\theta =1$) with probability of $\alpha$, the journal’s utility is $B-c$. However, if the manuscript’s quality is unacceptable ($\theta =0$) with probability of $1-\alpha$, the journal’s utility is $-c$. Hence, the journal’s expected utility is $U_l = \alpha B -c$ when the manuscript decision happens to be issued by a low-ability editor.

Now suppose the manuscript decision is issued by a high-ability editor. In the separating equilibrium of the real-life case, the high-ability editor does not send the paper to external peer reviewers and issues a desk-decision consistent with their private signal. Therefore, if the manuscript’s quality is acceptable ($\theta =1$) with probability of $\alpha$, the journal’s utility is $\rho _h B + (1-\rho _h)(-D)$. However, if the manuscript’s quality is unacceptable ($\theta =0$) with probability of $1-\alpha$, the journal’s utility is $(1-\rho _h)(-d)$. Thus, the journal’s expected utility is $U_h = \alpha [\rho _h B - (1-\rho _h)D] - (1-\alpha )(1-\rho _h)d$ when the manuscript decision happens to be issued by a high-ability editor.

By comparing the journal’s expected utilities $U_l$ and $U_h$, we find that the journal has a lower expected utility if the manuscript decision happens to be issued by a high-ability editor than if the manuscript decision had been issued by a low-ability editor if $U_h < U_l$, or equivalently, if the cost of the external review c is low enough

$$\begin{aligned} c < (1-\rho _h)[\alpha (B+D) + (1-\alpha )d]. \end{aligned}$$