The phrasing might be better in a different direction:
"...getting them to admit that Scandinavia is not doing something inherently wrong with it's high tax system, given that they have relatively high happiness and quality of life."
(in that right-wing conservatives state that high taxes inherently will cause reduction of standard of living/happiness)
"...getting them to admit that Scandinavia is not doing something inherently wrong with it's high tax system, given that they have relatively high happiness and quality of life."
There is another conservative argument against this: To acknowledge that it might actually be true that the average happiness is increased, but to reject the morality of it.
Too see why someone might think that, imagine the following scenario: You find scientific evidence for the fact that if one forces the minority of the best-looking young women of a society at gunpoint to be of sexual service to whomever wishes to be pleased (there will be a government office regulating this) increases the average happiness of the country.
In other words, my argument questions that the happiness (needs/wishes/etc.) of a majority is at all relevant. This position is also known as individualism and at the root of (American) conservatism.
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If you disregard the happiness of the women, anyway
This can be looked at as a form of deontology: govts don't have the right to tax anybody, and the outcomes of wisely spent taxation don't affect that.
No, it suffices if less women's happiness sacrificed are needed than the amount of men whose happiness will be increased (assuming the "amount of happiness" - whatever that is to mean in the first place - is equal per individual). Then you can regard the happiness of women and still score a net increase in happiness. That's the whole point of the argument.
I don't understand what you were saying in the second sentence.