That’s a question of psychology, not of rationality. I don’t know the answer, though my prejudices say it probably isn’t a great idea.
But there’s another reason why you might choose not to buy another in that situation: you may think it less likely than you did before that any given other mattress will solve your sleep problems—so now the deal you’re considering isn’t “$1400 for better sleep” but “$1400 for one more attempt at better sleep that may well fail like the last one did”. (That was really the deal you were considering all along, but you didn’t know it then.)
Also, now you’re $1400 poorer. If that’s a sizeable fraction of your wealth then $1400 is worth more to you now than it was before and that may very reasonably affect your willingness to spend that much on a mattress. If it’s not a sizeable fraction of your wealth, it may still be a sizeable fraction of your readily accessible wealth (the rest being tied up in pension schemes, investments you can’t liquidate very quickly, accounts or investments you could liquidate quickly but have a policy of not doing because otherwise you’d spend too much, future earnings[1], etc.) so you may not want to spend that much again soon.
[1] Of course, if you consider something like the estimated net present value of your future earnings as part of your wealth it’s much less likely that $1400 is a sizeable fraction of your total wealth thus reckoned.
So this may be a case where letting the sunk cost fallacy do its thing produces a better decision than trying to ignore sunk costs, if you aren’t very careful about it. I suspect there are quite a lot of such situations. Cognitive biases sometimes yield better approximations to optimal rationality than simple attempts at explicit unbiased reasoning...
That’s a question of psychology, not of rationality. I don’t know the answer, though my prejudices say it probably isn’t a great idea.
But there’s another reason why you might choose not to buy another in that situation: you may think it less likely than you did before that any given other mattress will solve your sleep problems—so now the deal you’re considering isn’t “$1400 for better sleep” but “$1400 for one more attempt at better sleep that may well fail like the last one did”. (That was really the deal you were considering all along, but you didn’t know it then.)
Also, now you’re $1400 poorer. If that’s a sizeable fraction of your wealth then $1400 is worth more to you now than it was before and that may very reasonably affect your willingness to spend that much on a mattress. If it’s not a sizeable fraction of your wealth, it may still be a sizeable fraction of your readily accessible wealth (the rest being tied up in pension schemes, investments you can’t liquidate very quickly, accounts or investments you could liquidate quickly but have a policy of not doing because otherwise you’d spend too much, future earnings[1], etc.) so you may not want to spend that much again soon.
[1] Of course, if you consider something like the estimated net present value of your future earnings as part of your wealth it’s much less likely that $1400 is a sizeable fraction of your total wealth thus reckoned.
So this may be a case where letting the sunk cost fallacy do its thing produces a better decision than trying to ignore sunk costs, if you aren’t very careful about it. I suspect there are quite a lot of such situations. Cognitive biases sometimes yield better approximations to optimal rationality than simple attempts at explicit unbiased reasoning...