To what extent can a Beit Din actually force someone to get married?

Question

In an answer on this site regarding the obligation to procreate, R. Hershel Schachter is quoted as saying (emphasis mine),

And although Beth Din could force someone to get married even if he did not want to, Beth Din would not force one to observe this mitzvah of having more children than the minimal two. This principle of Rabbi Yeshoshua is a statement of the proper mode of behavior (derech eretz) rather than an official rabbinic enachnent (takkanah).

In what way can a Beit Din "force" someone to get married against their will? Is this similar to the handling of get-refusers, in which a court is not able to actually issue the get, only apply increasing pressure on the husband to do so, or does a beit din actually have the authority to perform a valid marriage against the will of the soon-to-be-spouses?

Answer 1

R. Eliezer Melamed writes in Peninei Halakhah, Simhat HaBayit uVirkhato 5:8 (Hebrew) as follows:

• According to R. Yosef Karo, Beit Din can force a twenty year old man to get married either by beating him (Rif, Rambam) or by rebuking or fining him (Tosafot, Rosh) until he agrees to marry.
• In practice, this would only happen in rare cases, such as if a man was already involved with a woman and they had agreed to marry, but the man was pushing off the wedding without a good reason. Or, if a man wanted to marry a woman with whom he could not have children.
• According to Rivash and Rema, nowadays Beit Din never force someone to marry.

So, to directly answer your question, even according to the opinions that allow Beit Din to force a man to marry, they do so by pressurizing him, rather than actually contracting a marriage on his behalf against his will.

Answer 2

A Beit Din cannot force anyone to get married. The marriage must be "the joint voluntary actions of the man and the woman."

A Jewish wedding is a ceremony rich with layers of halacha and spiritual meanings and traditions. At the core of traditional Jewish marriage is the constitutive act of a marital relationship – the Maase Kinyan (literally 'Act of Purchase'): The man gives the woman a wedding ring and says to his bride in front of two witnesses, 'Behold, you are consecrated unto me by this ring, according to the law of Moses and Israel.' The marriage is thus constituted by the woman‘s willing acceptance of the ring. Similarly, a divorce is concluded by the willing transmission of a Get (deed of divorce) by the husband to his wife and her willing acceptance of the Get.

The validity of a marriage or a divorce depends entirely on the joint voluntary actions of the man and the woman. For this reason, the Batei Din adjudicates the validity of a marriages and divorces as questions of fact, but they cannot dissolve a marriage through an act of the court. Even in situations where a couple is under obligation to divorce because of some fault of one of the partners, all a Beit Din can do is order the husband to divorce his wife and impose sanctions on a party that refuses to cooperate. This is an important factor in the problem of the Agunah – a wife who is 'chained' to a husband who refuses to give her a divorce, even against the order of a Beit Din."

Miller, Akiva. (2014.) The Policing of Religious Marriage Prohibitions in Israel: Religion, State, and Information Technology, 31 J. Marshall J. Info. Tech. & Privacy L. 23