For a horror story of abuse of power see Takitota v. The Attorney General & Ors (Bahamas)  UKPC 12 (18 March 2009). How do the courts calculate how much money to give a person who has been unlawfully detained for years in inhumane and degrading conditions?
There are two aspects to consider: first, constitutional or vindicatory damages, and second, compensation for loss of liberty.
Exemplary damages are not appropriate where constitutional or vindicatory damages are awarded:
"15. Their Lordships consider that it would not be appropriate to make an award both by way of exemplary damages and for breach of constitutional rights. When the vindicatory function of the latter head of damages has been discharged, with the element of deterrence that a substantial award carries with it, the purpose of exemplary damages has largely been achieved. To make a further award of exemplary damages, as the appellant's counsel sought, would be to introduce duplication ... ."
The fact that constitutional or vindicatory damages are to be awarded should not affect the calculation of the compensatory damages. But, in calculating the amount appropriate for compensation for a lengthy period of unlawful detention (here it was over 8 years), the phenomenon of "tapering" comes into play.
"9. ... it is usual and proper to reduce the level of damages by tapering them when dealing with an extended period of unlawful imprisonment: cf Thompson v Commissioner of Police of the Metropolis  1 QB 498, 515, per Lord Woolf MR. ... ."
Tapering looks rather odd, but it is an established method of calculation. It is a bit like reducing a sentence for multiple offences on totality grounds to prevent the final sentence being out of proportion to the harm that the offender caused. But I think it is morally dubious. Is a person to receive less compensation because he may have become accustomed to inhumane treatment? Does the law grow weary of his claim? Don't the days become increasingly valuable, as they are each a greater proportion of his remaining life?
Here the Board upheld the amount awarded for constitutional or vindicatory damages, but remitted the question of compensatory damages to the Court of Appeal because that Court's judgment was imprecise and did not enable assessment of the correctness of its mathematics. The haphazard nature of tapering is illustrated where, after calculating compensatory damages on a dollars-per-day basis, the Court of Appeal continued:
"96. In light of the fact that the appellant will be receiving a lump sum [ie $100,000 for constitutional or vindicatory damages] we would reduce the figure for compensatory damages by $330,500.00 and award the sum of $400,000.00 as compensation for the loss of 8 years and two months of the appellant's life. We will not, however, reduce the sum of $100,000.00 by way of exemplary damages since that sum is awarded to show the strong disapproval of the courts for the conduct of the respondents in this case from the time of the appellant's arrest until this case is finally disposed of."
Why chop off $330,500? The Court was wrong to use constitutional damages as the reason for doing this, but how much will it take away as "tapering"? The Privy Council thought the local court better placed to set the amount of compensation, but one wonders.