The first number you hear tends to stick

An opening figure is not just information, it is a peg, and every later estimate quietly gathers around it.

You walk into a shop with no idea what a kettle costs. The first one you see is marked at ninety dollars. Everything afterwards is judged in relation to that: sixty seems reasonable, forty seems a bargain, a hundred and twenty seems steep. Had the first tag read thirty, the identical sixty dollar kettle would feel like an extravagance. The starting figure did no work at all in establishing what a kettle is worth, and yet it shaped every judgement that followed, and did so without ever presenting itself as an argument.

The pull works with numbers that are transparently arbitrary, which is what makes it worth taking seriously. A figure that arrives first, from any source, gives the mind somewhere to stand while it forms an estimate, and standing somewhere is more comfortable than standing nowhere. This is why an opening offer matters so much in any negotiation, and why a budget mentioned early in a conversation tends to become the shape of the conversation regardless of what anyone actually needs. Notice too that the peg does not have to be a price. A first estimate of how long a job will take, offered casually by whoever spoke first, will quietly govern every schedule built afterwards.

The defence is to form your own number before you are exposed to anyone else's. What would I pay for this, before I look at the tag. What do I think this job is worth, before they say. It will be a rough figure and often a poor one, but it is yours, and it gives the later number something to be compared against rather than absorbed into. When you have not had that chance, the fallback is to notice the first figure out loud, name it as arbitrary, and then deliberately consider a value well away from it in both directions.