Two things get justified before data collection in a Bayesian workflow: the prior (via transparent elicitation) and the sample size (via the precision the posterior will achieve, not a long-run p-value). This page makes both concrete.
Instead of guessing α and β, answer two questions a reviewer will ask: What is my best guess for the true proportion? and How confident am I (how much "prior data" is my belief worth)?
Set a half-width for your 95% credible belief; this finds the prior strength that matches. Leave to "0.4" default.
A defensible prior is a stated belief. The exact phrase for a methods section: "We specified a Beta(α,β) prior, eliciting a best guess of p̄ with a strength of n₀ pseudo-observations (equivalently, a 95% credible interval of [lo, hi])." This is the transparent, reviewer-safe way to disclose assumptions (O'Hagan et al., 2006; Kruschke, 2015, Ch. 5).
Planning by posterior precision: set the half-width you want for your 95% credible interval of θ, propose a prior and an expected observed proportion, and see the needed n. This is the modern alternative to frequentist power that doesn't depend on a magical p-value threshold.
0 = uninformative Beta(1,1). With an informative prior you need fewer respondents.
Precision planning ≠ frequentist power. We target the width of a 95% credible interval, a quantity you can interpret directly. This sidesteps the criticized Neyman–Pearson power conventions (see Kruschke & Liddell, 2018; the ASA's 2016 statement on p-values, Wasserstein & Lazar).