Scaling language model size yields diminishing returns for single-message political persuasion

In a preregistered survey experiment conducted in April to May 2024, we recruited US adults online ($N=25,982$) and measured the extent to which they agreed or disagreed with one of 10 contemporary US policy issue stances. The set of policies covered a range of issue areas (e.g., immigration, healthcare, employment, foreign policy, criminal justice); for more details, see Issue Stances. Before giving their opinion, respondents were randomly assigned to one of three groups: AI, human, or control. Those in the control group gave their opinion without being exposed to a persuasive message; those in the human or AI group were exposed to a single persuasive message of 150 to 250 words written by human researchers or by one of 24 different language models, respectively. In total, 720 messages were generated across all language models. The outcome was issue stance agreement, measured using a four-item question battery. Persuasive impact was computed as the difference in the mean outcome between treatment and control groups (for further detail see Experiment Design).

Following our preregistered protocol, we first fit a random-effects meta-analysis to estimate the relationship between language model size and persuasiveness—adhering to the analytic procedure outlined in previous work (30) (for details, see Statistical Analysis). The key covariate in the meta-analysis is the natural logarithm of each language model’s parameter count, which we center to facilitate estimation as well as to allow interpretation of the intercept term as the estimated persuasiveness of a language model of average size in our sample. We specify the intercept as a random effect across individual persuasive messages, language models, and political issues and specify the parameter count covariate as a random effect across political issues (Statistical Analysis).

The key results of our meta-analysis are given by its fixed effect estimates and are as follows. First, we find that the language models are persuasive on average: the estimated value of the intercept is 5.77, indicating that people exposed to a message generated by a language model of average size in our sample (37.9B parameters) changed their attitudes 5.77 percentage points on average toward the issue stance being advocated by the message (Table 1). Second, we find that the persuasiveness of a language model is positively associated with the natural logarithm of its number of active parameters. Specifically, we estimate that a one-unit increase in the logarithm of a model’s parameter count is linearly associated with an increase of 1.26 percentage points in its average treatment effect (Table 1 and Fig. 1A). The key implication of this finding is that language models’ persuasiveness is characterized by diminishing returns, such that current frontier models—Claude-3-Opus and GPT-4—are only slightly more persuasive than models which are smaller in size by an order of magnitude or more (Fig. 1B). This point is underscored by direct contrasts between the specific models in our sample, which show that those with as few as 7 to 13 billion parameters (Qwen1.5-7B and Llama-2-13B) are similarly persuasive as the frontier models (estimated $<$300B parameters) and human benchmark (Fig. 2).

Importantly, we perform a series of robustness checks and additional analyses on these key results. First, we fit two further meta-analyses in which we estimate a quadratic and cubic term for the log of the parameter count covariate, respectively, in addition to the linear term. This serves as a test of whether these more flexible versions of the log-linear function better capture the relationship between language model size and persuasiveness. However, we do not find any evidence that the quadratic or cubic terms significantly predict model persuasiveness beyond the linear term (SI Appendix, Table S4).

Second, since the true size of the frontier language models in our sample (GPT-4-Turbo and Claude-3-Opus) is unknown [unconfirmed reports put their size at around 1.7 trillion parameters (31, 32)], for our primary analysis, we assumed a conservative lower-bound size of 300B parameters. However, our results are robust to a range of alternative assumptions about the size of these models; in SI Appendix, Fig. S4 we show that we obtain substantively similar results with assumed parameter count values up to and beyond 1T for these models.

Third, it could be that differences between model families account for our results, rather than differences in model size per se. Thus, we fit an additional meta-analysis with a fixed effect for model family, but our key result remains robust in this analysis (SI Appendix, Table S7).

Fourth, the smallest language model in our sample (Pythia-70M) is something of an outlier—for example, participants were much more likely to identify messages from this model as coming from an AI model (SI Appendix, Fig. S3). Thus, we repeat our primary analysis excluding the data from this model; our results are robust to this exclusion (SI Appendix, Table S8).

Finally, we also explore whether the association between language model size and persuasiveness is better characterized by other common nonlinear functions used to model diminishing returns, beyond the log-linear function we fitted in our preregistered analysis. Specifically, we explore power law, saturating growth, logistic, and log-logistic functions (for further details, see SI Appendix, section 4.5). These exploratory analyses were not preregistered. To facilitate estimation and comparison of these more complex nonlinear functions, we do not use the random-effects meta-analytic estimator applied to the message-level effects, as in our primary analysis. Rather, we use nonlinear least squares regression applied to the raw (i.e., person-level) attitude data. Thus, the fitted values of the functions are mean attitude levels rather than treatment effects. However, to facilitate comparison with the functional form from our preregistered analysis (log-linear), we also estimate the log-linear function using the nonlinear least squares estimator.

Fig. 3 shows the fitted values of these functions (for the estimated parameter values of each function, see SI Appendix, section 4.5 and Table S5). The raw mean attitude in each language model group is also overlaid in Fig. 3, and a horizontal line indicates the mean attitude in the control group (recall that participants in the control group did not receive any message from a language model). We compare the fit of each function in two ways. First, we examine their AIC and BIC values (Table 2). Second, we implement leave-one-language-model-out cross-validation to calculate the average prediction error of each function (Table 2, for further detail see SI Appendix, section 4.5).

Across these metrics, the log-logistic function fits the data best, though the improvement over some of the other functions is not dramatic. For example, the BIC values and cross-validation errors are similar across all but the saturating growth function—though the ΔAIC between the log-logistic function and the other functions ranges from approximately 3 to greater than 10 (Table 2); values that indicate moderate-to-substantial differences in model performance according to some rules of thumb (33). Notably, the best-fitting log-logistic function implies sharper diminishing returns to language model size than the log-linear function we estimated in our preregistered analysis above.

To intuitively understand the extent of diminishing returns implied by this best-fitting log-logistic function, we perform an extrapolation exercise: we extrapolate the function to 3T (trillion) and 30T parameters—up to two orders of magnitude more parameters than the assumed upper-bound in our sample (300B). This exercise implies that a message generated by a 3T and 30T model would be only slightly more persuasive ($<$1 percentage point and 1.25 percentage points, respectively) than that generated by a 300B model (SI Appendix, section 4.11).

Finally, we again emphasize that GPT-4 and Claude-3-Opus could be much larger in size than the conservative lower-bound estimate of 300B parameters we assumed in our preregistered analysis. Thus, we repeat our exploratory analysis of alternative nonlinear functions above, this time assuming these frontier language models are of size 1.7T parameters (32). Under this less-conservative assumption, the log-logistic and logistic functions obtain yet further support relative to the alternative functions (e.g., ΔAIC values of 15 to 25, see SI Appendix, section 4.5.1 and Table S6), indicating that the implications of this exploratory analysis are robust to different assumptions about the (unconfirmed) size of the frontier models in our sample.

Thus far we have uncovered evidence that model persuasiveness is subject to diminishing returns as a function of model size. Our analysis suggests that, in our setting (single-message political persuasion), we may soon reach an effective ceiling on the returns to scaling the size of current language models.

In a second set of analyses, we use our dataset to explore potential reasons why larger language models are more persuasive in this setting. These exploratory analyses were not preregistered.

Specifically, we started by scoring each message and model on a range of different features, including message length (word count), type-token ratio, Flesch-Kincaid readability score, proportion of moral language (34), and proportion of emotional language (35) (Message Features and Task Completion). For example, perhaps larger models are more persuasive because they use more emotional or moral rhetoric (36, 37) or because they write longer, more detailed messages than smaller models—thereby providing more new information (38) or causing greater message elaboration among the audience (39). We also scored each model for the extent to which it simply completed the task we asked of it (i.e., to generate messages on a particular topic). To do so, we scored each message for its legibility—i.e., punctuation, grammar, etc.—and whether it was on-topic—i.e., wrote about the issue we prompted, and advocated for the specific position on the issue that we requested (i.e., for or against, see Message Features and Task Completion).

In a first analysis step, we then use these features to predict the persuasiveness of the language models. We find that, of these features, task completion score is the only statistically significant predictor of persuasiveness (Fig. 4A; full model results in SI Appendix, Table S6); and, in particular, follows a nonlinear association such that models with task completion scores of 2 or less (out of 3) are estimated to be entirely unpersuasive, while scores between 2.5 and 3 are strongly associated with persuasiveness (Fig. 4B). This result highlights the possibility that the larger language models in our sample might derive their persuasive advantage from their superior ability to follow instructions; that is, writing coherent on-topic messages. In other words, task completion could mediate larger models’ persuasive advantage. While our design is not specifically set up to identify mediation (40, 41), we can nevertheless evaluate some of its minimally necessary conditions. For example, at minimum the potential mediator (task completion score) must also be associated with language model size. We clearly observe this in our data; larger models more reliably completed the task we asked of them (Fig. 4C). Notably, the frontier models in our sample are at the maximum value of the task completion score—they write entirely coherently and always stay on topic.

In a final step, we adjust for task completion score in our primary meta-analysis of language model size and persuasiveness. Thus, this analysis asks: once we condition on models’ ability to generate coherent, on-topic messages (i.e., their task completion score), is model size still associated with model persuasiveness? We find that the answer is no: when we adjust for task completion score, the association between model size (log of parameter count) and persuasiveness shrinks toward zero and is no longer statistically significant (Fig. 4D). Notably, however, task completion score remains a statistically significant predictor of persuasiveness in this analysis (SI Appendix, Table S5).

In sum, we find that, among various features of the language models, basic task completion is the only one that is associated with both model size and model persuasiveness. Furthermore, statistically adjusting for this feature notably shrinks the association between language model size and persuasiveness toward zero, a pattern consistent with mediation. However, making strong inferences about mediation is deeply challenging (40, 41), and, as mentioned above, our design is not specifically set up for that purpose. For example, one possibility is that the task completion score could simply be correlated with other potential mediating variables that we did not measure, but is not a mediating variable itself. Given this, we draw the following conclusion from the above exploratory analyses: insofar as mere task completion is a true mediator of the relationship between language model size and persuasiveness, then our results suggest that larger models of the future will derive limited additional persuasive advantage from it—for the key reason that current frontier models are already at ceiling on this metric in our setting (Fig. 3C). Consequently, insofar as further scaling model size cannot further improve upon this feature, this would provide additional reason to expect diminishing returns to size in our persuasion setting.

In this paper, we estimated the association between language model size and model persuasiveness. Our results offer evidence of sharply diminishing returns, such that current frontier models are barely more persuasive than models which are smaller in size by an order of magnitude or more. Moreover, the data highlight mere task completion (coherence and staying on topic) as a potential mediator of larger models’ persuasive advantage. Taken together, these findings contrast with recent speculation from across academia and industry that the single-message persuasiveness of existing transformer-based architectures could continue to increase rapidly with model size and instead suggest the possibility of an imminent effective ceiling on the persuasiveness of static LLM-generated messages. Specifically, our results suggest that a newly released model trained using existing techniques and architectures may not offer significant persuasive advantage over existing models or human baselines-even if it is orders of magnitude larger in size. Given our setting, we expect these results to hold for single-message political persuasion (e.g., email, text, brief article, social media post, pamphlet), when the model has not been explicitly fine-tuned for persuasiveness, and when the model does not have any particular context or information about the message reader.

In addition to documenting evidence of diminishing returns to model size, our study offers an exploratory comparison of several different functions to describe these diminishing returns. Of the functions we explore, a log-logistic function fits the data best (though, as noted, the magnitude of the improvement over other log-linear functions depends somewhat on estimated size of frontier models). As we describe above, extrapolating this function implies that larger language models of the future may be only slightly more persuasive than current frontier models on the order of a single percentage point (SI Appendix, section 4.11). By way of contrast, had the diminishing returns been best described by a power law function (for example), the same extrapolation exercise implies that larger language models of the future would be considerably more persuasive than current frontier models perhaps by as much as 5 percentage points (SI Appendix, section 4.11). In politics, the difference between 1 and 5 percentage points can be highly consequential (e.g., for electoral outcomes). Although we emphasize that our comparison of these functions is exploratory and there remains uncertainty, the fact that the best-fitting scaling function was log-logistic aligns with recent theoretical work in other domains (42). Nevertheless, future research can provide additional evidence to further distinguish between specific functions for best capturing the diminishing returns to model size in our persuasion setting.

Importantly, our findings do not imply that LLM-generated messages are unpersuasive; on the contrary, we find that even models which are orders of magnitude smaller than the current state-of-the-art are capable of reaching human-level persuasiveness. Further, our results show that fine-tuning a pretrained model on just 10K examples from a commonly available open-instruction-tuning dataset was sufficient to match the persuasive impact of llama-2-7B-instruct, a model which was fine-tuned using Meta’s extensive proprietary posttraining procedures. Additionally, the two API-accessible frontier models we evaluated readily generated messages that were among the most persuasive across all models. Together, these findings suggest that the cost and complexity of training or accessing a persuasive language model is lower than might have previously been assumed, potentially broadening the range of actors capable of using LLMs for influence campaigns or attempts at mass attitude change.

We also note that in the present work, we made no attempts to explicitly train or optimize our models for persuasiveness. While this allowed us to mitigate safety concerns and ensure that our findings generalize to commonly available instruction-tuned language models, it also means that in absolute terms, the persuasiveness ceiling we estimate here (approximately 12 percentage points in aggregate across issues) could be higher for models which are explicitly trained for a persuasion task. Our findings may therefore constitute a lower-bound on the absolute persuasive impact actually achievable via single LLM-generated messages (even if the scaling relationship is as we document here).

We found that adjusting for task completion score rendered model size a nonsignificant predictor of persuasiveness, consistent with task completion functioning as a mediator of the model size–persuasiveness relationship. However, it is important to emphasize that inferences of mediation are challenging to draw with confidence (43, 44), and that our experiment was not designed specifically to maximize the validity of such inferences. In particular, both model size and task completion score are observed (not randomly assigned) variables in our design and are thus subject to all the usual concerns regarding confounding by other, unobserved variables. The implication of this is that, while our results are consistent with the aforementioned mediation pattern, this inference should be held lightly and subject to additional empirical scrutiny in future research.

This research was approved by the Oxford Internet Institute’s Departmental Research Ethics Committee (reference number OII_C1A_24_012) and preregistered on Open Source Framework. Informed consent was obtained from all participants. All code and replication materials are publicly available in our project Github repository. For additional study materials consult our SI Appendix.

The following section outlines our experimental methods, including model selection, instruction-tuning, message generation, issue-stance selection, experimental procedure, and statistical analysis.

For helpful comments and suggestions, in no particular order, we thank Lujain Ibrahim, Chris Summerfield, Luke Hewitt, Hannah Rose Kirk, Felix Simon, Laura Ruis, and Adriana Stephan, as well as seminar audiences at the University of Cambridge and Royal Holloway, University of London. This work was partially supported by the Ecosystem Leadership Award under the Engineering and Physical Sciences Research Council (EPSRC) Grant EPX03870X1, The Alan Turing Institute, and the UK AI Safety Institute. This work was also supported in part by Baskerville: a national accelerated compute resource under the EPSRC Grant EP/T022221/1, and The Alan Turing Institute under EPSRC Grant EP/N510129/1. We also acknowledge support from Prolific. P.R. was supported by a Ministero dell’Università e della Ricerca - Framework per l’Attrazione e il Rafforzamento delle Eccellenze 2020 initiative under Grant Agreement Prot. R20YSMBZ8S (INDOMITA) and the European Research Council under the European Union’s Horizon 2020 research and innovation program (No. 949944, INTEGRATOR).