Option Bounds in a risk-averse incomplete market

I was reading the article "On option pricing bounds" by Ritchken(1985).

It uses linear programming to determine options upper and lower bounds.

Given a single period model, the stock price will have n states. ie.($$s_1,s_2...s_n$$)

According to the law of one price, the stock price can be written as $$S_0=\sum_{j=1}^n s_je_j$$ where $$e_j$$ is the current price of a pure state j security that pays out 1 at time T if state j occurs. (ie. $$e_j$$ is state-contingent claim )

We now assume that investors are risk-averse, and there exists a set of ex ante consensus probabilities ($$\pi_i$$)for the states. Specifically, we have $$e_j=\pi_jd_j$$ And since investors are risk-averse, so $$d_1\geq d_2 \geq d_3 ... \geq d_n \geq 0$$.

And my question is why $$d_1\geq d_2 \geq d_3 ... \geq d_n \geq 0$$ must hold when investors are risk-averse?