In an open and inclusive poly network, where regular testing is done before a new partner is added, I maintain that more people does not necessarily = more risk, as long as those people do, in fact, require tests beforehand and do, in fact, notify all people when an incidence does come up.
If you have 3 people in a group, he believes, this is inherently safer than having 5 people in a group because that is two more people who the group has to monitor to ensure they are following the safety rules.
However, if you have 3 people in a group, one of whom is prone to cheating or taking on partners without testing first, I state that this is inherently more dangerous than a group of 5 people who have shown a consistent pattern of testing and notification. As the number of people rises, at least within a certain range, the risk level does not, in my opinion, significantly increase when all people consistently use regular testing and disclosure.
To illustrate my point, a couple of researchers actually wrote a book about it. Well, they wrote a book about sexuality and within the book was a segment on HIV risk for a variable number of partners. It's called With Pleasure: Thoughts on the Nature of Human Sexuality by Paul R. Abramson & Steven D. Pinkerton. The premise of this math formula is that each person's HIV status is unknown and the partners are randomly selected from the population at large.
According to the calculations (which use math symbols that I can't enter here because I write in plain text editors), "the risk resulting from 100 protected [sexual] contacts is about the same as that arising from only 10 unprotected [sexual] contacts". They go on to say:
"For sexually active individuals with more than one partner, the situation is slightly more complicated. Although the probability of becoming infected as a result of sexual contact with any one of these partners can be calculated using [this equation], the rules of probability calculus prevent us from simply adding them together to arrive at the overall risk of infection. ...The part that really impacts the poly community is that all of these scenarios and formulas are done with choosing a partner totally at random from the entire population without knowing his or her HIV status. With regular condom use, regular testing, and open and honest communication about status, the probability of becoming infected with HIV drops to a very small number close to zero. With a known status of HIV-negative, and no exposure to HIV since testing, the probability drops to a small number close to zero even without the condoms.
As might be expected, the probability of infection arising from N one-night stands is greater than the risk from N contacts with a single partner (monogamy). However, the difference is not nearly as great as one might suppose. ... the relative risk reduction achieved by engaging in N sexual contacts with a single partner rather than N one-night-stands is greater in the high infectivity condition (a=0.01) and increases as the number of one-night stands gets large, but is less than 40% in any case. In contrast, the relative risk reduction due to the consistent use of condoms is about 90% regardless of the infectivity or number of partners. In other words, in this situation even the most dramatic change in the number of sexual partners - from 100 to 1 - provides LESS protection than does the simple expedient of always wearing a condom.
These results highlight the inadequacy of educational programs that focus on getting people to limit the number of sexual partners as a means of reducing HIV risk. Although there are conditions for which this is sound advice (such as populations with a high prevalence of HIV and other STDs) the simple strategy of always using condoms is usually a superior means of reducing risk. ...
Finally, to return to the question posed at the beginning of this discussion: is everyone at risk? Obviously that depends on her sexual behaviour, including who she has sex with, what kind of sex, and whether or not her partners wear condoms for penetrative activities. For the sake of argument, suppose the infectivity is 1 in 1,000 and she selects 10 male partners at random from a population in which 1 out of every 200 men is infected with HIV. If she has intercourse 100 times with each of these men and never uses condoms, she faces an infection risk of 0.0047 (in other words, out of 211 such women, we would expect one to become infected with HIV as a consequence of her sexual behaviour). If, instead, she and her partners used condoms for every act of intercourse, her risk would be reduced by about 90%, to 0.0005 (1 out of 2010)."
This, of course, only affects those STDs that are fluid-borne, like HIV. The incidence of contact-borne STDs like Herpes is only partially reduced by condom use, not the 90% quoted above. And for the untestable or hard-to-test STDs like HPV, I assume we cannot significantly lower the incidence rate by changing the variable from "unknown status" to "known status", but none of that was discussed.
Anyway, this book sounds pretty fascinating and I plan to pick up a copy sometime soon. One of the other thoughts they propose in the book is that the primary purpose of sex has evolved to be pleasure and procreation is a by-product. When I did a search for the title, I didn't find any negative reviews of the book, no blog entries claiming they're hacks and peudo-scientists, so I'm curious to see the research they used to reach this conclusion. Here's the link to read what I quoted above, just click on the cover image and you will access a preview of the book that you can scroll through: https://amzn.to/2IInG7n