Algorithmic fairness in Artificial Intelligence, or AI, encapsulates the notion that machine learning algorithms and systems should be free from bias and should offer equally balanced outcomes for all users, independent of race, gender, socioeconomic status, or other distinguishing characteristics. This aspect of AI engineering underscores the necessity of fairness and ethics in the development and deployment of AI systems, focusing primarily on equal and unbiased treatment and results.

Several distinctive attributes characterize Algorithmic fairness in AI:

• Representation Parity: This concerns ensuring that the data or examples used to train the model adequately represent all relevant groups. The data used in AI needs to be free from inherent bias, ensuring the model does not discriminate or unfairly favor any particular group.

• Predictive Parity: AI models must accurately predict the outcomes without any form of bias towards or against certain groups. It implies that the likelihood of an event's occurrence for a specific group should be the same as the likelihood predicted by the model for that particular group.

• Unawareness: This principle states that the AI model should not be designed to depend or rely upon particular sensitive attributes, such as race, religion or gender of the user.

A successful implementation of Algorithmic fairness in an AI system requires careful selection of the fairness definition that aligns with the system's intended use. Also, it necessitates a critical assessment of the training data to detect and correct any inherent biases.

Monitoring the AI system's outputs for evidence of discrimination and continually updating the system to correct identified biases is crucial. To ensure fairness, it is also imperative to develop strategies that ensure transparent decision-making in AI systems.

The deployment of AI models that adhere to the principles of algorithmic fairness presents several significant advantages:

• Ethical and Equitable Decision Making: AI models, when developed with fairness in mind, can make decisions that are balanced and impartial. This eradicates the potential for biased results and penalties against user groups based on their characteristics.

• Improved User Confidence: When AI systems are designed for fairness, user trust in the technology is significantly bolstered. Users can rely on the outputs with increased confidence knowing that they are not being discriminated against.

• Reduced Legal Risks: Deploying AI systems that consistently deliver fair decisions can help organizations avoid critical legal issues. Compliance with regulatory guidelines around anti-discrimination can be more straightforward, reducing liability risks.

• Expansion potential: AI systems embedded with fairness can adapt dynamically as societal norms and definitions of fairness change. It ensures the system's longevity and continued relevance.

However, algorithmic fairness in AI systems does not come without its set of inherent limitations and challenges:

• Ambiguity in Fairness Definitions: The varied interpretations of what constitutes 'fairness' can pose a considerable challenge. Depending on the context, different definitions of fairness may be appropriate, making it complex to design a universally fair algorithm.

• Data Bias: AI models can only be as fair as the data used to train them. Existing societal bias present in the data can inadvertently introduce bias into the AI system.

• Lack of Transparency: AI models, specifically deep learning models, can be inherently opaque and hard to interpret. This makes it challenging to recognize and rectify biases in their decision-making process.

• Compromised Accuracy: Striving for fairness in an AI system may at times require a trade-off with accuracy. Crafting an algorithm that provides equal outcomes for all users could compromise the accuracy of predictions or analyses for each specific group.

In conclusion, achieving algorithmic fairness in AI systems is not a one-time activity but requires a constant commitment to fairness, inclusivity, and the elimination of bias at every step of development and deployment. It is an essential consideration in the design and application of AI, ensuring that its benefits are enjoyed by all, without discrimination.