Sentiment analysis (also known as opinion mining) is a branch of Natural Language Processing (NLP) and Machine Learning that focuses on deciphering and understanding emotions and opinions present in text data. This powerful tool, when applied to political texts, can deliver insightful analysis by helping to determine the polarity of sentiment (positive, negative, or neutral) attached to political issues, policies, candidates, or parties.

• Applicability: Sentiment analysis can be applied to a broad spectrum of political texts such as speeches, debates, social media posts, opinion columns, and more. These sources provide raw data for analytics, possibly impacting political perceptions and decisions.
• Extraction of emotion: By using sentiment analysis, one can decipher the emotions and explicit as well as implicit meanings embedded in political texts through computational linguistic techniques.
• Real-time analysis: With the advancement in computing power, it is possible to analyze large volumes of text data in real-time – this can be particularly valuable during campaigns or election periods.
• Scalability: As political texts and opinion data continue to grow exponentially, sentiment analysis algorithms that can efficiently manage and analyze large datasets are vitally important for broad and comprehensive analysis.
• Cost-effective: Deploying sentiment analysis over maintaining traditional surveys and polls can be significantly more affordable and resource-saving, while providing richer and more diverse insights.

• Critical Insight: Sentiment analysis can provide crucial insights into public opinion about specific issues, candidates, or political parties. This information can help strategize political campaigns and make informed decisions.
• Unbiased nature: Unlike human assessment, sentiment analysis can impartially interpret large volumes of data, reducing human bias in the decision-making process.
• Efficient and Expeditious: Automated sentiment analysis tools can quickly process large volumes of text, yielding faster results than human analysts. This enables real-time decision-making based on live data.
• Versatility: Sentiment analysis can process and analyze diverse sources of text, from social media feeds to news articles, press releases, speeches, and more.
• Evolution tracking: Sentiment analysis can track shifts in public sentiment over time, aiding in the prediction of future electoral behavior and policy acceptance.

• Contextual misunderstanding: Algorithms may find it challenging to accurately interpret context, potentially misjudging sentiment where irony, sarcasm, or localized expressions are used.
• Subtlety handling: Subtle expressions of sentiment or neutral statements may be wrongly classified, leading to inaccurate analysis.
• Dependence on language resources: Sentiment analysis quality is deeply contingent on the richness of language resources and datasets available. Languages or contexts underrepresented in available datasets may lead to weaker analysis.
• Algorithmic biases: Despite being more objective than human analysts, sentiment analysis tools may inadvertently inherit biases present in the text data used for training.

A thorough implementation process of sentiment analysis in political texts requires the precise study of organizational needs and the selection of an appropriate sentiment analysis model. Following this is a cost-efficacy evaluation, alongside an assessment of whether the available data and technologies align with the organizational needs. The successful deployment of sentiment analysis depends upon careful planning, methodical review, and custom-made solutions to meet your specific demands. Hence, the ongoing embracing, monitoring, and reviewing of these deployment processes become crucial.