As an associate editor, you're not just reviewing papers for content, but also for technical soundness. You've come across an algorithm that you believe is weak, and your analysis has revealed a better approach. Now, you're faced with a dilemma: do you have an obligation to share your findings with the higher-level editors, or can you keep them to yourself?
Let's break this down. You've identified a flaw in the proposed algorithm and have a proof that a simpler, brute-force approach outperforms it. You're recommending rejection of the paper, which is a reasonable decision given the technical shortcomings. However, sharing your proof could add an extra layer of confidence to your recommendation, especially if the higher-level editors are not familiar with the technical details.
From a purely technical standpoint, you don't have an obligation to share your proof. As an editor, your primary responsibility is to ensure that the paper is sound from a technical perspective. If your analysis is thorough and your recommendations are based on solid evidence, that's all that's required. However, there are a few considerations to keep in mind.
First, consider the purpose of the editor position. You've been hired to review papers and provide technical feedback. Sharing your proof could be seen as part of that duty, even if it's not explicitly required. On the other hand, if you're simply looking to improve your own result, sharing your proof could be seen as overstepping your bounds.
Another factor to consider is the dynamics of the editorial process. If you share your proof, it could be seen as a way to establish credibility and demonstrate your expertise. This could be particularly relevant if you're working with a team of editors, where trust and confidence are essential. However, if you're dealing with a hierarchical structure, where decisions are made by higher-level editors, sharing your proof might be seen as unnecessary or even presumptuous.
Ultimately, the decision to share your proof is up to you. If you do choose to share it, make sure you're doing so in a way that's clear, concise, and respectful of the editorial process. You might consider sending a brief summary of your findings to the higher-level editors, or including it as an appendix to the paper. Either way, be sure to keep your motivations in mind and be transparent about your role as an editor.
It's worth noting that, in some cases, editors may be asked to provide additional information or support for their recommendations. If you're unsure about what's expected of you, don't hesitate to ask for clarification. And remember, as an editor, your primary responsibility is to ensure that the paper is sound from a technical perspective. If you're confident in your analysis and recommendations, that's all that's required.
One final thought: if you do decide to share your proof, be prepared for the possibility that it might be met with skepticism or even criticism. As an editor, you're not infallible, and your analysis may not be perfect. But that's okay – it's all part of the process. The important thing is to be transparent, respectful, and professional, even in the face of disagreement.