# Using Options Framework to think about where to submit a paper

Posted on Sun 04 January 2015 in Random Thoughts

Suppose that the probability of acceptance at the best journal is $$p$$ and at the 2nd best journal is $$\theta p$$. Moreover, after a paper has been reviewed once, we have the chance to improve it and consequently increase the probability of acceptance. Let these 2nd chance probabilities be $$\lambda p$$ and $$\lambda\theta p$$ respectively. Then, the value from “best-2nd best” sequence is given by

$$V_{1} = \left( {1 + \epsilon} \right)p + 1\left( {1 - p} \right)\lambda\theta p$$

and the value from the reversed option is given by

$$V_{2} = \theta p + \left( {1 + \epsilon} \right)\left( {1 - \theta p} \right)\lambda p$$

The second best followed up best is optimal iff

$$\theta p + \left( {1 + \epsilon} \right)\left( {1 - \theta p} \right)\lambda p \geq \left( {1 + \epsilon} \right)p + 1\left( {1 - p} \right)\lambda\theta p$$

That is, there exists a $$\hat{p}$$ such that when $$p < \hat{p}$$ implies that second best followed by best is optimal.

So if the paper is not too good, then start off sending it to second best, and then if needed send it to the top journal. And if the paper is great, then start with the top journal and then if needed send it to the second best journal.