"I am a little cautious about London, though, as many people seem to leave there for the same reasons they leave Australia or other parts of the UK."
What the user is saying
The destination-choice heuristic Nathan is implicitly applying: "if a destination's emigrants share the complaints of people in your current home, you've selected an exit pattern, not a destination." This is a useful, non-obvious filter — it assumes the failure mode has a structural cause (cost, weather, lifestyle saturation, distance from nature, social disconnection) rather than a personal one.
Why this is interesting as a mental model
A standard relocation heuristic is "go where the people you admire live." The Nathan heuristic is the inverse: exclude places where the people who left share your current complaints. That's a negative filter — it cuts the search space before you start comparing features.
San Francisco: would fail on cost (Sydney is also expensive); partially fails on distance-to-nature. The user's heuristic, applied.
Budapest / Prague / Tallinn: do not fail this filter. People leaving those cities leave for family / different climate / different career — not the same complaints as Sydney-leavers.
Lisbon: a borderline case. Lisboa-leavers sometimes name cost (Lisbon got expensive fast) and grey weather, but the failure mode is different in kind from Sydney-leavers (financial migration to Lisbon changed the city, rather than Sydney being inherently X).
Counter-cases
"Exit pattern" ignores who enters the city. A place whose leavers complain of X can still be a great home for someone who's never lived with X. London attracts people who want the art, finance, ecosystem; it repels people who want sun, space, and quiet. Both can be true.
The heuristic overshoots at the margin. A negative filter applied too aggressively excludes cities that have 80% of the complaints but 100% of the upside on the axis that matters (Lisbon for some people, Vancouver for others).
Operational version of the heuristic
"Before committing to live somewhere, ask: do the people who leave this place complain of the same things I'd leave Sydney for? If yes, find a different city."