that is only an assumption. Indeed, you should always keep in mind the difference between Asset Allocation and Capital Allocation. You can see Asset Allocation as the first step of making investments, where you want to decide which securities will provide you with meaningful risk-return characteristics. Of course, Markowitz allocation is the stronghold here and the risk-return characteristics is mean-variance. In a second step, after gotten the efficient risk-return combinations, then comes into play the individual degree of risk aversion. In fact, here each investor would choose a different combination of securities that will deliver a different risk-return profile. From the first step also comes Merton '71 idea of Two funds separation theorem, when the market portfolio and the risk free asset exists and returns come from a geometric brownian motion. If you see the separation Asset Allocation - Capital Allocation should be clearer why you want to keep the assumption of sharing same degree of risk aversion in the first step, because you want to evaluate the investment opportunities objectively (Asset Allocation) to then allocate capital (capital allocation) subjectively only in a second moment.

That is only an assumption. Indeed, you should always keep in mind the difference between Asset Allocation and Capital Allocation. 

You can see Asset Allocation as the first step of making investments, where you want to decide which securities will provide you with meaningful risk-return characteristics. Of course, Markowitz allocation is the stronghold here and the risk-return characteristics is mean-variance. 

In a second step, after you've gotten the efficient risk-return combinations, then comes into play the individual degree of risk aversion. In fact, here each investor would choose a different combination of securities that will deliver a different risk-return profile. 

From the first step also comes Merton's 1971 idea of Two funds separation theorem, when the market portfolio and the risk free asset exists and returns come from a geometric Brownian motion. 

If you see the Asset Allocation/Capital Allocation separation it should be clearer why you want to keep the assumption of sharing the same degree of risk aversion in the first step, because you want to evaluate the investment opportunities objectively (Asset Allocation) to then allocate capital (capital allocation) subjectively only in a second moment.