A member of the British Parliament is reputed to have said, “The first purpose of good social reform is to increase the sum total of human happiness.
Conclusion
The reform I propose is a good social reform.
Evidence (Since)
The reform I propose would make my constituents happy.
Intermediate Conclusion (so)
Any reform which makes somebody happy is achieving its purpose.
Evidence
The first purpose of good social reform is to increase the sum total of human happiness.
Evaluate
This argument draws two conclusions (the first indicated by the conclusion indicator So, the second indicated by the support indicator Since).
We could potentially weaken the argument by attacking either move.
The "So" conclusion is mangled interpretation of the initial rule stated. She said that the .
Our author then takes that to mean Any reform that makes even one person happy is achieving its purpose.
Hold the phone, there, author. We said "the FIRST purpose, not the only purpose". Maybe a reform could meet the first purpose but fail to meet the second/third/fourth purpose and therefore not qualify as good social reform.
More importantly, the standard was whether the sum total (the net effect) was an increase of happiness. It wasn't whether "at least one person's happiness increased".
After all, if a new reform increases the happiness of the richest 0.1% but lessens the happiness of the remaining 99.9% of the population, it hasn't increased the sum total of human happiness.
The conclusion drawn in the last sentence seems like valid logic, within the logically invalid world of the author. If we accept her flawed Intermediate Conclusion, that , then we'd accept that this author's reform meets the first purpose of good social reform.
But, naturally, we do not accept the author's Intermediate Conclusion.
Finally, there is a gap between "achieving the first purpose of good social reform" and assuming something therefore "is a good social reform".
Maybe you could meet the first purpose of something but still not be considered that thing.
Goal
There were several complaints there, so we have to stay flexible. The most likely objection I would be looking for is the wide gap between , which fails to consider that as one person's happiness goes up, there might be other people's happiness going down.