Select the correct option: Without her prompt intervention, the discussion might well have ___ into an acrimonious stalemate.

The correct option is devolved.

Step-by-Step Explanation:

1. Analyze the Context of the Sentence:
The sentence discusses a "discussion" that was at risk of becoming an "acrimonious stalemate" (a bitter and angry deadlock). The phrase "Without her prompt intervention" implies a negative trend or deterioration that was successfully prevented.

2. Examine the Option Definitions:
• abstained: Formally declined to vote or chose not to do something. This does not fit the context of a discussion transforming into a stalemate.
• devolved: Degenerated, deteriorated, or passed down into a lower or worse state (often used as "devolved into"). This perfectly describes a discussion deteriorating into a bitter stalemate.
• emerged: Came into view or became apparent. It does not carry the negative connotation of worsening or deteriorating into a conflict.
• ejected: Forcefully expelled or thrown out. It does not fit grammatically or contextually with "into an acrimonious stalemate."

3. Conclusion:
The word devolved fits both contextually and grammatically with the preposition "into" to mean deteriorating into a worse situation.