With the popularity of online shopping and the enhancement of consumers' low-carbon preference, while taking into account the impact of fairness concern on manufacturers' competitive optimal decision-making, this paper establishes a platform supply chain decision-making model consisting of an ordinary manufacturer, a low carbon manufacturer and an e-commerce platform, and makes a comparative analysis of the equilibrium decision-making under the circumstances that the ordinary manufacturer does not have fairness concerns, and has advantageous inequity aversion and disadvantageous inequity aversion. Under disadvantageous inequity aversion,the service cost sharing contract is proposed to improve the supply chain performance. The results show that: 1) The low carbon level increases in consumers' low-carbon preference and price competition while decreases in commission rate of e-commerce platform. 2) Manufacturers' profits are affected by consumers' low-carbon preference. When consumers' low-carbon preference is lower than a certain threshold, the profits for the ordinary manufacturer is higher than that for the low-carbon manufacturer; vice versa. 3) The ordinary manufacturer considering advantageous inequity aversion will improve pricing, low-carbon level, service level as well as overall supply chain performance, but reduce consumer surplus and social welfare. 4) Although that the ordinary manufacturer considering disadvantageous inequity aversion will reduce pricing, low-carbon level, service level and the overall performance of the supply chain, consumer surplus and social welfare can be improved, and the service cost sharing contract can be performed to realize the Pareto improvement for the low carbon level, the profit of the manufacturers and the e-commerce platform.