Because he is a non-dom, he pays tax on his UK earnings as normal but does not pay UK tax on overseas earnings as long as that money stays abroad. Recently, an annual fee was introduced in lieu of the normal taxation on such overseas earnings that a normal UK resident would have to pay. Is that what was agreed he would pay when he was made a peer? At the time of writing, nobody appears to know.
If it is, that means that the best case that can be made for Michael Ashcroft is that he has been sitting in the legislature of a country whose taxes he does not pay because that country is not the place he considers home. (And the leader of the political party that he funds with the money he might otherwise have paid in taxes declares that using that money to win the election is a “patriotic duty” … but that’s another story.)
The underlying problem exposed by the Michael Ashcroft scandal (other than the idea that a place in the legislature can be simply given to a businessman by a committee rather than won in an election, which is also another story) is that taxes are levied on a national basis but the income and wealth upon which those taxes are levied are mobile and move freely around the world. And the richer you are, the more mobile your money can be.
The fact that money might be earned in one territory by someone who lives in another territory is no reason to tax that money twice, but it is no reason to exempt that money from tax, either. The proliferating network of intergovernmental tax treaties goes some way towards evening up the way that taxes are levied internationally, but there are still too many tax havens for anyone to be comfortable with. After all, it only takes one hole in a pipe for all the water to drain out.
There are some people who argue that taxation is a fundamental matter of national sovereignty. They are wrong; it is not. It is merely another aspect of government that, in the modern, interdependent world in which we now find ourselves, needs to be organised on a multi-level basis if it is to be both effective and appropriate to the circumstances. It would be a pity if the fuss about somebody exploiting a loophole in the tax rules were to overshadow this bigger issue.