The cause of less poverty effect more able to get food, shelter, health care, education
The cause of more able to get food, shelter, health care, education effect more happy one
The cause of more happy one effect less thief, fighting and killing
The cause of less thief, fighting and killing effect more peacefulness in outer environment
The cause of more peacefulness in outer environment effect more happiness on the rich one
The cause of more peacefulness in outer environment effect also the rich one more able to obtain more wealth
The cause of the rich one more able to obtain more wealth effect even more wealth to the rich one
The cause of even more wealth to the rich one effect even more happiness to the rich one

Hence,

Less poverty on the poor = More wealth and happiness on the rich one

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