1.  Introduction

In the profound changes of the Web 3.0 era, data-driven recommendation systems have become the core engine for social media information dissemination. While reshaping the way the public obtains information, they have also quietly caused serious problems of cognitive imbalance [1]. The evolution trend of public opinion is increasingly dominated by algorithms [2]. In this context, the phenomenon of polarization of public opinion is becoming increasingly prominent [3], which not only erodes the public space for rational discussion, but also harbors deep-seated concerns of shaking social consensus and causing social tearing [4]. Algorithmic bias is not a simple concept with a single dimension, but rather a hidden value orientation and uncertainty in the construction of algorithmic models [5-6]. Polarization of public opinion is a dynamic process in which different social groups gradually move towards opposing extremes in terms of viewpoints, emotions, and identity recognition [7-8]. As a public opinion arena, social media shapes the generation and evolution trajectory of public opinion [9].

In the research context of algorithmic bias, there has been a paradigm shift from technology neutrality to value loading. Early studies often viewed algorithms as purely technical tools [10], but as research deepened, scholars gradually realized that algorithms embedded developers' value judgments [11]. In the study of the formation mechanism of public opinion polarization, theories such as filter bubbles have revealed the impact of information environment on group differentiation, but there are also certain limitations [12]. The polarization amplification effect of existing models, such as collaborative filtering algorithms, has been partially empirically validated, but there is still room for further exploration of the systematic and complex mechanisms [13].

Based on this, this article focuses on the impact of algorithmic bias on social media public opinion polarization. By constructing a multidimensional analysis model, it reveals the significant positive impact and threshold effect of algorithmic bias on public opinion polarization, and clarifies the differentiated pathways of algorithmic bias in different dimensions. In theory, this article deepens the understanding of the complex relationship between algorithmic bias and public opinion polarization, providing a systematic analytical framework and empirical basis for related research; In practice, this article helps to understand the evolutionary laws of social media public opinion ecology, providing targeted reference directions for alleviating public opinion polarization, maintaining rational public space, and social stability.

2.  Research design

2.1.  Research framework construction

When deconstructing the complex relationship between algorithmic bias and public opinion polarization, a single disciplinary perspective can easily fall into methodological traps. This article is based on the structured theory of systems science and communication studies, and constructs a multidimensional analysis model with the following expression:

$$ Polarizatio{n}_t=f\left(SNA\right(Ne{t}_{t-1}),CC(Alg{o}_t,Use{r}_t),{\epsilon }_t)$$(1)

Among them, SNA (⋅) is a social network analysis function; CC (⋅) is a computational propagation function; ε_t is the system noise term.

The core logic lies in the dynamic evolution process of public opinion polarization, which is the independent variable of algorithm bias, the mediating variable of user cognitive behavior, and the moderating variable of social network structure, through a three dimensional deconstruction mechanism.

Algorithmic bias has a nonlinear amplification effect on user cognition. Algorithmic bias implants initial bias seeds into the user cognitive system through the interaction between Selective Exposure and Cognitive Heuristics. The dual filtering expression for information filtering is as follows:

$$ \mathit{Pr}(Exposure\left|Algo\right)=\frac{e^{\alpha \cdot Similar+\beta \cdot Emotional}}{e^{\gamma \cdot Diversity}}$$(2)

Among them, S_similar is the weight of content similarity, E_emotional is the intensity of emotional arousal, and D_diversity is the diversity penalty factor (α, β, γ are platform preset parameters)

Based on the attention based bounded rationality model, the processing depth δ c of biased content by users shows a marginal increasing effect, expressed as follows:

$$ {\delta }_c=\lambda \cdot \mathit{log}(1+\omega \cdot \text{Bia}{\text{s}}_{\text{intensity}})$$(3)

Where λ is the cognitive elasticity coefficient.

2.2.  Data collection and processing

This study constructs a three-stage funnel-shaped data collection system, ensuring sample representativeness through cross platform complementary strategies. The specific dataset collected is shown in Table 1.

2.3.  Variable definition

The main variables and definitions involved in this article are shown in Table 2.

2.4.  Model construction

The benchmark model expression is as follows:

$$ Polarizatio{n}_{it}={\beta }_0+{\beta }_{1}AlgoBia{s}_{it}+{\beta }_2(AlgoBia{s}_{it}\times H{I}_{it})+{\sum }_{k=1}^{K_1}{\gamma }_{k}Contro{l}_{kit}+{\mu }_i+{\lambda }_t+{\epsilon }_{it}$$(4)

The expression of the nonlinear extended model is as follows:

Among them, i is the user/community unit, and t is the weekly time slice (t=1,2,..., 52); μ i is the individual fixed effect; λ t is the time fixed effect; θ is the critical value of algorithmic bias intensity.

3.  Result

3.1.  Main effect

The main effect results are shown in Table 3, and Model 4 indicates that cognitive narrowing reinforces the effect of algorithmic bias. Model 5 reveals a threshold effect, where the AlgoBias effect is not significant in the low bias area, but significantly increases in the high bias area, and HI and interaction terms remain significant. This indicates that there is a critical value for the impact of algorithmic bias, and the effect amplifies sharply after exceeding it. The moderating effect of cognitive factors remains stable.

3.2.  Mechanism verification

The results of the mechanism test are shown in Table 4, and all three have passed statistical tests, confirming the differential mechanism of different dimensions of algorithmic bias on public opinion polarization.

3.3.  Sub dimensional evolution

The sub dimensional evolution results are shown in Table 5, where Ediv increased from 1.62 to 2.37, an increase of 46.3%. The Wilcoxon test is significant, indicating a significant increase in the degree of polarization of content stance; The increase in Δ Q reached 162.5%, and the SAOM model showed highly statistically significant changes, reflecting the severe polarization of the network structure; Bc increased from 0.31 to 0.59, an increase of 90.3%, and the K-S test was significant, indicating a significant improvement in the polarization of emotional distribution.

As shown in Figure 1, all three have passed strict statistical tests, confirming the comprehensive and significant intensification of public opinion polarization in terms of content, structure, and emotional dimensions.

4.  Conclusion

This study found that algorithmic bias has a significant positive impact on social media public opinion polarization, and there is a threshold effect. The impact of high bias areas is much stronger than that of low bias areas, and cognitive narrowing will strengthen this effect; Data level, model level, and feedback level biases act on polarization through different paths, with content stance, network structure, and emotional distribution polarization significantly exacerbated, with network structure polarization showing the greatest increase; The cross platform robustness test confirms the reliability of the above conclusion and reveals the systematic mechanism of algorithmic bias catalyzing public opinion polarization.