We don’t know yet. This article is the discussion of a possibility. But it may be the case that the earliest vaccine(s) are not effective enough to allow people to decide for themselves whether or not to take it. Before you object, let me explain.
Ideally, a vaccine would be 100% effective, meaning none of those persons who get the vaccine can get the disease. In such a case, it would be fine to let 10 or 20% of the population decide not to take the vaccine.
But that’s not how vaccines work. Often vaccines are far from 100% effective, and so some vaccinated persons can still contract the illness. That’s not too much of a problem, from the point of view of protecting society as a whole, due to herd immunity. If 90% of the population is vaccinated, then the other 10% are protected because 90 out of 100 persons around them can’t give them the disease as they have been vaccinated. The chances that the 10 out of 100 persons who are able to get sick, will be sick, and will give the non-vaccinated person the disease are low. So everyone is protected from a vaccine that is 100% effective given to 90% of the population. And a 90% effective vaccine given to 90% of the population also still does well.
What if the vaccine is only 60% effective, like the best of the recent flu vaccines? You have a percentage of persons who are not vaccinated, and then a percentage of those who are vaccinated, but who get sick anyway due to the low effectiveness of the vaccine. The result is a percentage that is too low for herd immunity.
At this point, things get a little complicated. The herd immunity threshold (HIT) differs for different diseases. For measles, it’s over 90%; for SARS, it’s 50 to 80%; for flu, it’s about 40%. So for measles, which is highly contagious, herd immunity only kicks in with 90% of the population vaccinated. Measles vaccines should therefore be mandatory, or herd immunity is greatly reduced. But flu vaccines only need 40% participation to obtain herd immunity, and that threshold can be met with a voluntary vaccination. We don’t know the HIT for Covid-19, but it might be higher than SARS, as the Spike protein for SARS-CoV-2 has 10 times the binding affinity for ACE2 as SARS-CoV-1 had. If it is higher than SARS, we have to ask what percentage of the population will refuse a vaccine?
UPDATE 7/1/2020: A new study  found that the reproduction number (how many persons are newly-infected by each patient with Covid-19) was 2.6 without a lockdown, and 1.57 with a lockdown: “pre lockdown reproduction number as 2.6 (95% CI=2.34, 2.86) and post lockdown reduced to 1.57 (95% CI=1.3 , 1.84) implying effectiveness of the epidemic response strategies.”  However, they also state that: “The herd immunity is estimated between 36 to 61% for R0 of 1.57 and 2.6 respectively.” So without a lockdown, the effectively vaccinated would need to be 61% (e.g. a 75% effective vaccine accepted by 81.3% of the population, ultimately protects only 61% of the population).
People reject a vaccine for varying reasons. Some persons are afraid it is a scam from big pharmaceutical companies to make money. Other persons distrust the government. Some religious persons scrutinize the way a vaccine was developed, and reject any vaccine that used an aborted fetal cell line in some way. Sometimes young persons think themselves to be invulnerable, because they lack the experience of having suffered much in their lives.
Then there are political influences. If the Trump administration promotes a vaccine, some liberals might reject the vaccine for its association with him. The opposite effect could occur for a vaccine under a subsequent democratic president.
Finally, there is the influence of the mass media and the internet. Sometimes an opinion takes root in those forms of media (e.g. excessive insistence on RCTs and peer-review), and they will reject something in a reactionary manner, without a fair evaluation of the pros and cons. A wave of negative reactions in media could influence many persons not to accept the vaccine.
As for whether the vaccine should be mandatory, from a medical point of view, if a vaccine has low effectiveness and many persons would not accept it voluntarily, the vaccine would need to mandatory to obtain herd immunity. That is simply how the math works. Whether or not a mandatory vaccine is legal or moral is another question. But it should be discussed in public forums before a societal decision is made.
Some people might take the attitude, “Well, I’m getting the vaccine, and so I’ll be protected. Then let other people choose not to be protected. I don’t care.” That’s the wrong attitude because of the need to read herd immunity threshold. If the vaccine is 50% effective, and you’re the only one vaccinated, you have a 50% change of contracting a deadly disease. And because everyone around you is unprotected by the vaccine, anyone might give you that disease. But if everyone takes the 50% effective vaccine, it becomes more than 50% effective. For you to get the disease from someone, they would have to first contract it. Their odds of getting the disease (in this oversimplification) are 50%, then only if they get the disease would you have a 50% chance of getting it, making your odds of contracting the disease 25%, not 50%. I have way oversimplified the math here, but the principle is correct. The more persons who are vaccinated, even with a vaccine of limited effectiveness, the lower your risk of getting sick. If almost everyone is vaccinated, a 50% effective vaccine becomes much more effective than 50%. So it matters to everyone else, if you decide to take the vaccine. “No man is an island, entire of itself.”
Then there is another consideration. If you get sick, society has to care for you. And society is harmed, if you get sick and then spread the disease. For Covid-19, the number of persons who will be infected by each sick person is high, it is at least 2 or 3, and it may be much higher without a lockdown. You are making a decision for other people, not only for yourself. (So, get the vaccine.)
The vaccine needs to be as effective as possible. Failing that, the vaccine will need to be mandatory, in part to make up for its limited effectiveness. And if people refuse to be vaccinated, they need to be pressured to be vaccinated. The pressure could be very limited, and should certainly not include jail time or heavy fines. A modest amount of pressure will change the minds of persons who are rejecting the vaccine for reasons which are not very firmly held. Then those with very firm convictions against the vaccine can simply continue to refuse, and if so, they should not be forced.
What I am saying here is that, if a mandatory vaccine becomes necessary, it should be limited in its mandate. “Take the vaccine, or else you will incur this negative consequence of limited weight.” And the burden of that weight should be such that people with strong feelings or reasons against the vaccine, they can bear that weight without being crushed by it. Under this type of “mandatory” vaccine, some persons will still refuse, and that’s okay. We can tolerate a limited number of persons who absolutely refuse the vaccination.
There are some good reasons for a mandatory vaccine. But there should also be the possibility of absolute refusal for those who cannot accept it in good conscience. So I’m proposing a compromise between “do whatever you want” and “you absolutely have to accept this”.
Here’s a good article in the New England Journal of Medicine on 6 criteria that must be met before a vaccine should be made mandatory: Ensuring Uptake of Vaccines against SARS-CoV-2. I agree with these criteria.
Ronald L. Conte Jr.
Note: the author of this article is not a doctor, nurse, or healthcare provider.
1. Patrikar, Seema, et al. “Incubation Period and Reproduction Number for novel coronavirus (COVID-19) infections in India.” medRxiv (2020).