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I found one 2009 review by Snyder and Anderson that attempted to answer your question, i.e. whether external coercion makes a difference in therapy outcomes. From its sheepish abstract, you can probably guess that no firm conclusion can be drawn. The review is narrative, not systematic, although they do split their discussion by field of intervention: domestic violence, child abuse, incest, and substance abuse.

Alas most of the papers cited in there fall in two categories: those that (like your question) cast doubt on the outcomes from a theoretical perspective, or are empirical papers that don't directly compare voluntary to mandated therapy outcomes, but rather present correlational evidence why mandated therapy is a good idea. For example, in the case of domestic abuse, the number of abusive incidents is inversely correlated with the length of stay (number of sessions) in therapy. And--so the logic goes--it's better to have the batterer stay in therapy for longer no matter how that's achieved. But there's not a single paper cited in that section that directly evaluated the contrast you want (mandatory vs self-initiated). The same can be said for child abuse and incest, areas in which there's hardly any self-initiated therapy.

Only in the area of substance abuse there are some direct contrast papers, but most are of rather low quality and varying methodology and thus have fairly contradictory results:

While some outcome research reports that mandated clients did better than voluntary clients (Chopra, Preston, & Gerson, 1979; Dunham & Mauss, 1982), others (Smart, 1974) report that voluntary clients fared better. The majority, however, have found similarly beneficial outcomes for both groups (Anglin, Brecht, & Maddahian, 1989; Brecht, Anglin, & Wang, 1993; De Leon, 1988; Flores, 1983; Freedberg & Johnston, 1978; Hubbard et al., 1989; McGlothlin, 1979; Watson, Brown, Tilleskjor, Jacobs, & Pucel, 1988). Illustrative of these findings was a study by Anglin et al. (1989), who found that outcomes (length of stay in treatment, posttreatment gains) did not differ for addicts with legally coerced versus voluntary treatment entry. They suggested that given these findings, it made little sense to promote a social policy that allowed drug-dependent individuals to choose when to enter treatment and when to leave. Instead, a less costly and more efficient process would be to implement a more externally constraining system that does not rely on the individual’s fluctuating motivational state. In a literature review covering up to the year 2000, Miller and Flaherty (2000) concluded that the preponderance of the literature confirms the efficacy of mandated addiction treatment and that coercion helped motivate clients to comply with treatment. The inconsistent findings that have emerged in this literature may be due to the fact that outcome research in the area of substance abuse treatment has suffered from various methodological shortcomings (Howard & McCaughrin, 1996; Rotgers, 1992; Shearer, 2000). These include differences in outcome measures (e.g., measuring recidivism rates rather than client drinking levels, measuring employee job performance rather than level of substance use) and differences in comparison groups (e.g., comparing young, mandated, relatively healthy individuals with voluntary, older, chronic addicts). Differences may also be due to definitional inconsistencies as to what constitutes a mandated client (De Leon, 1988; Rotgers, 1992), addicts’ personal characteristics that affect response to treatment (such as the existence of personality disorders), or variations in treatment plans (Anglin et al., 1989). Others point to the inevitable problem of lack of control groups and random assignments (Howard & McCaughrin, 1996) and selection or recruitment bias (Dunham & Mauss, 1982). As it is virtually impossible to secure random assignment to treatment conditions, any quasi-experimental design which is implemented will be unable to definitively determine which effects on the outcome variable are due to treatment effects, rather than preexisting differences in the groups such as severity of the drinking problem, age, education, or social class. Finally, others point out that treatment programs vary widely and thus program sources of variance obscure the measurement of treatment effectiveness for legally referred clients (Inciardi, 1994). In what has been described as one of the only research studies that has tried to address many of these methodological problems, and ‘‘probably the best designed and executed study of coercion and treatment outcome to date’’ (Rotgers, 1992), Walsh et al. (1991) compared results of three treatment options for employees referred by their employee assistance plan for alcohol problems (compulsory inpatient; mandatory Alcoholics Anonymous [AA] meetings only; or voluntary option to do either). The employees were randomly assigned to these treatment programs and followed for 2 years. All three groups were found to have improved in terms of job functioning and reduced drinking, with the inpatient clients faring the best. As the employer could back up the referral to treatment with firing if drinking continued, the researchers opined that clients’ motivation for succeeding in the more intensive inpatient condition might have been confounded with employer coercion. Research shows that length of time in treatment affects outcome, and mandated clients do appear to remain in treatment longer than voluntary clients (De Leon, Melnick, & Tims, 2001; Goldsmith & Latessa, 2001; Leukefeld & Tims, 1988; Satel, 2000). In an interesting study, Dunham and Mauss (1982) compared the differential rates of alcoholism treatment success rates for courtmandated and voluntary clients in a community alcoholism treatment center, statistically controlling for pretreatment differences. Clients were divided into four groups: self-referrals, informal agency (AA, physician) referrals, driving while impaired (DWI; court) referrals, and other legal⁄ court referrals. While it was found that certain socioeconomic traits had a powerful impact on outcome (i.e., no prior treatment experience, active employment, education, not dependent on social assistance, stable marriage and family life), type of referral was a stronger predictor of outcome. The more coercion that was applied, the better the outcome. Treatment success was greater for those referred from the justice system than those attending voluntarily. The success rate for DWI clients was almost double that of voluntary clients (43% vs. 22%). The authors concluded that the certainty of the consequences for noncompliance with treatment for the DWI clients, and their having the most to lose (as they had the best occupations, highest education, etc.), was an important factor. Dehmel, Klett, and Buhringer (1986) also found that more socially integrated clients (e.g., employed, stable home, and family life) had a greater likelihood of completing treatment.

And ultimate reason posited for this is that time in therapy seem to beat other considerations, allowing even a voluntary kind of self-motivation to emerge:

the research literature suggests that what mandated clients may lack in terms of initial motivation may be more than compensated for by their tendency to stay in treatment longer than their voluntary counterparts, allowing time for intrinsic motivation to develop and therapeutic techniques to take effect. Length of time in treatment affects outcome, and mandated clients appear to remain in treatment longer than their voluntary counterparts. [...] We have found no research to date that has examined whether the strength of the [therapeutic] alliance or the mandated versus voluntary referral status is more predictive of outcome. This would seem to be a topic worthy of investigation.

But perhaps for substance abuse (the only area where apparently there's enough research for the contrast you want) it does seem to look like "time in therapy trumps everything else" (with the caveat that it may be mediated by actually building a therapeutic alliance...) at least based on this review, which being a narrative one has non-trivial potential for bias.