There are Pareto-improvements: everyone is made better off by their own standards. There are, similarly, Pareto-worsenings: Everyone is made worse off by their own standard, or their welfare is unchanged.
Then there are Kaldor-Hicks improvements, which happen if one e.g. reallocates the available goods so that the better-off could compensate the now worse-off to create a Pareto improvement. This compensation need not occur, it needs to be merely possible.
Now can there be a Kaldor-Hicks-worsening?
The naive version (everyone is worse (or equally well) off, and there is no way of making a single person better off through redistribution) seems too strong, there is probably always a redistribution that gives the available resources to a single agent.
A simple negation of the criteria, then perhaps makes more sense: A change is a Kaldor-Hicks-worsening if and only if everyone is worse (or equally well) off and there is no way of creating a Pareto-improvement through reallocation.
This implies a anti-Kaldor-Hicks-worsening: A change makes everyone worse off, but there is some reallocation that creates a Pareto improvement.
Example: We have a Sadist and a Masochist. The Masochist starts hurting the Sadist, thus creating opportunity cost for them both. Switching the roles creates a Pareto improvement.
There are Pareto-improvements: everyone is made better off by their own standards. There are, similarly, Pareto-worsenings: Everyone is made worse off by their own standard, or their welfare is unchanged.
Then there are Kaldor-Hicks improvements, which happen if one e.g. reallocates the available goods so that the better-off could compensate the now worse-off to create a Pareto improvement. This compensation need not occur, it needs to be merely possible.
Now can there be a Kaldor-Hicks-worsening?
The naive version (everyone is worse (or equally well) off, and there is no way of making a single person better off through redistribution) seems too strong, there is probably always a redistribution that gives the available resources to a single agent.
A simple negation of the criteria, then perhaps makes more sense: A change is a Kaldor-Hicks-worsening if and only if everyone is worse (or equally well) off and there is no way of creating a Pareto-improvement through reallocation.
This implies a anti-Kaldor-Hicks-worsening: A change makes everyone worse off, but there is some reallocation that creates a Pareto improvement.
Example: We have a Sadist and a Masochist. The Masochist starts hurting the Sadist, thus creating opportunity cost for them both. Switching the roles creates a Pareto improvement.