llm-consensus 0.1.0
Langchain-compatible deliberation and consensus framework using multiple LLMs.
License: MIT
Requires Python: >=3.11

# Consensus

**Consensus** is a Langchain-compatible framework that enables deliberative decision-making among multiple LLMs (Large Language Models). It supports parallel execution, multiple rounds of reasoning, peer feedback, and customizable strategies like majority vote, weighted confidence, and ranked choice.

---

## ✨ Features

- 🔄 Combine multiple LLMs' answers for a final consensus  
- ⚙️ Strategies: `majority`, `weighted`, `ranked`  
- 🔁 Multi-round deliberation (automatic or fixed rounds)  
- 🗣 Peer feedback: each model can see what others answered  
- 🧠 Uses `Runnable` chains (`prompt | llm`) – fully compatible with Langchain 0.2+  
- 🧾 JSON export of all responses, rounds, and reasoning  

---

## 🚀 Installation

```bash
pip install git+https://github.com/jersobh/consensus.git
```

Or if installing from a local clone:

```bash
Copiar
Editar
git clone https://github.com/jersobh/consensus.git
cd consensus
pip install -e .
```

## 🧪 Example 

```python
from langchain.prompts import PromptTemplate
from langchain_community.llms.fake import FakeListLLM
from consensus.core import Consensus
import asyncio

prompt = PromptTemplate.from_template("""
Q: {question}

{peer_answers}

Please answer as fully and clearly as possible.
""")

llm1 = prompt | FakeListLLM(responses=["Answer A."])
llm2 = prompt | FakeListLLM(responses=["Answer B."])
llm3 = prompt | FakeListLLM(responses=["Answer A."])

engine = Consensus(
    llms=[llm1, llm2, llm3],
    strategy="majority",
    rounds=None,  # Runs until agreement
    enable_peer_feedback=True
)

async def run():
    result = await engine.get_consensus("What is the capital of France?")
    print("Final consensus answer:", result)
    print("\\nDeliberation Report:")
    print(engine.report.to_json())

if __name__ == "__main__":
    asyncio.run(run())

```


## 📊 Strategies
|Strategy|Description|
|---|---|
|majority  |	Picks the most frequent final answer|
|weighted  |	Uses confidence scores (if provided)|
|ranked    |    Aggregates ranked preferences|


## ➡️ Output:

❓ Question: 
```
A single-phase lighting circuit has an installed power of 1,100 VA and runs inside a PVC conduit embedded in a masonry wall. 
Alongside it, insulated conductors from another circuit are present. The conductors are copper, the ambient temperature is 35°C, and the voltage is 220 V. Determine the conductor's cross-sectional area and the circuit breaker's nominal current for this circuit.
```

💡 Answer: `The conductor's cross-sectional area should be 2.5 mm² and the circuit breaker's nominal current should be 10 a.`

🗫 Discussion:

```json
{
  "rounds": [
    {
      "round": 1,
      "responses": [
        {
          "answer": "The conductor cross-sectional area should be 2.5 mm\u00b2 and the circuit breaker's nominal current should be 10 A.",
          "reason": "Here's the breakdown:\n\n1.  **Calculate the current (I):**\n    *   Apparent Power (S) = 1100 VA\n    *   Voltage (V) = 220 V\n    *   I = S / V = 1100 VA / 220 V = 5 A\n\n2.  **Determine the cable characteristics:**\n    *   Conductor Material: Copper\n    *   Installation Method: PVC conduit in a masonry wall (allows for higher current carrying capacity than, for example, free air installation)\n    *   Ambient Temperature: 35\u00b0C\n    *   Number of loaded circuits: 2 (the lighting circuit + another circuit nearby, so we need to consider grouping derating)\n\n3.  **Consider Derating Factors:**\n    *   **Ambient Temperature Derating:**  Refer to the appropriate cable sizing tables (e.g., from IEC 60364 or relevant national standards like the NEC, BS7671).  For 35\u00b0C ambient temperature, the derating is minimal or non-existent for many common cable types. Let's assume it doesn't require significant derating for this example, as the temperature is not significantly above the standard reference temperature.\n    *   **Grouping Derating:** Since there are other circuits present, we need to consider grouping.  Without more information about the number of circuits bundled together, we'll make a conservative assumption.  Refer to the cable sizing table for the appropriate derating factor. A common derating factor for two circuits grouped is around 0.8.  This means the cable's current carrying capacity must be higher to compensate for the heat generated by the other circuit.\n\n4.  **Calculate the Required Current Carrying Capacity (I_req):**\n    *   I_req = I / (Derating factor) = 5 A / 0.8 = 6.25 A\n\n5.  **Select the Conductor Size:**\n    *   Consult the cable sizing tables to find a copper conductor size with a current carrying capacity greater than or equal to 6.25 A, considering the installation method (PVC conduit in masonry). A 2.5 mm\u00b2 copper conductor is typically rated for a current carrying capacity well above 6.25 A, even with derating.\n    *   From standard tables, a 2.5 mm\u00b2 copper conductor in PVC conduit is typically rated to well over 10 A (e.g., 24 A for a single circuit). Therefore, a 2.5 mm\u00b2 conductor is suitable.  Check your local wiring regulations to confirm the exact current-carrying capacity for the specific cable type used.\n\n6.  **Select the Circuit Breaker:**\n    *   The circuit breaker's nominal current should be greater than the calculated circuit current (5A) and less than the cable's current carrying capacity (which is significantly larger than 5A, due to the conductor size selected). This is to protect the cable from overload.  A standard circuit breaker rating that satisfies this is 10 A. A 6A breaker would also work, but 10A is more common. The circuit breaker should be chosen to protect the cable and the connected load. The breaker should also be sized to allow for the inrush current of the connected appliances or lighting.  In most cases, a 10A breaker will be fine for a 5A load.  Always check your local wiring regulations."
        },
        {
          "answer": "To determine the conductor's cross-sectional area, we need to use the formula for calculating the allowable current-carrying capacity of a conductor.\n\n  I = (VA / V) / (1.2 * Pf * kA * kC * kF) * kG\n\n  Where:\n  I = the allowable current-carrying capacity of the conductor (A)\n  VA = the installed power (VA)\n  V = the voltage (V)\n  Pf = the power factor (1 for resistive loads)\n  kA = the ambient temperature correction factor\n  kC = the conductor correction factor\n  kF = the number of conductors correction factor\n  kG = the grounding correction factor\n\n  Given values:\n  VA = 1100 VA\n  V = 220 V\n  Ambient temperature = 35\u00b0C\n  Conductor material = Copper\n\n  We need to find the conductor's cross-sectional area (mm\u00b2) and the circuit breaker's nominal current (A).\n\n  The conductor correction factor for copper (kC) is 0.83.\n  The number of conductors correction factor (kF) is 1.15 (for 3 conductors in a masonry wall).\n  The grounding correction factor (kG) is 1 (assuming a well-grounded system).\n\n  Using the ambient temperature of 35\u00b0C, the ambient temperature correction factor (kA) can be found from the IEC 60287 table:\n  kA = 0.85 (for 35\u00b0C)\n\n  Now, we can calculate the allowable current-carrying capacity of the conductor:\n  I = (1100 / 220) / (1.2 * 1 * 0.83 * 1.15 * 1) * 0.85\n  I \u2248 3.37 A\n\n  However, this value is below the standard allowable current-carrying capacity for copper conductors (IEC 60287). To determine the cross-sectional area, we need to refer to the IEC 60287 table or use an online calculator.\n\n  Let's assume we have used an online calculator or the IEC 60287 table to find the cross-sectional area (A) corresponding to an ambient temperature of 35\u00b0C and the allowable current-carrying capacity of around 3.37 A.\n\n  The result shows that the conductor's cross-sectional area is approximately 2.5 mm\u00b2.\n\n  The circuit breaker's nominal current should be slightly higher than the calculated current-carrying capacity of the conductor to account for inrush currents and other factors. A common practice is to use a circuit breaker with a nominal current of 80-100% of the conductor's current-carrying capacity.\n  Therefore, the circuit breaker's nominal current for this circuit is approximately 3.37 * 1.2 = 4.04 A or the next standard value of 4 A or 5 A.\n\n  The final answer is 2.5 mm\u00b2 for the conductor's cross-sectional area and 4 A or 5 A for the circuit breaker's nominal current.",
          "reason": "The calculation is based on the IEC 60287 standard for the allowable current-carrying capacity of copper conductors in a masonry wall, considering the ambient temperature, conductor material, and other relevant factors."
        },
        {
          "answer": "{\"conductor_cross_sectional_area\": \"1.5 mm\\u00b2\", \"circuit_breaker_nominal_current\": \"10 A\"}",
          "reason": "To determine the conductor cross-sectional area and circuit breaker's nominal current, we must consider several factors: the installed power, ambient temperature, and voltage. The circuit has a total power of 1,100 VA and operates at 220 V, so the current (I) can be calculated using the formula: I = P / V = 1,100 VA / 220 V = 5 A.\n\nConsidering that the circuit is installed with other circuits in a conduit, a derating factor due to the grouping of cables and elevated ambient temperature must be applied. Referring to standard electrical installation guidelines (such as the IEC 60364 or national equivalents), a common practice is to use a derating factor of approximately 0.8 due to the two conditions (multiple circuits in conduit and 35\u00b0C ambient temperature instead of the 30\u00b0C that standard tables are often based on).\n\nThus, the adjusted current would be I_adj = 5 A / 0.8 = 6.25 A. For safety and compliance with standards, we typically select the next available conductor size that can handle this adjusted current. In most residential installations, a 1.5 mm\u00b2 copper conductor is chosen, as it can safely carry about 15 A to 18 A under typical installation conditions even after derating.\n\nFor the circuit breaker, since the load current is 5 A, and considering we choose a breaker to protect against overcurrent more than just the regular load current, a 10 A circuit breaker nominal current is typically selected for a circuit of this nature. This aides in providing margin for transient conditions and ensuring the safety under the typical power usage."
        }
      ]
    },
    {
      "round": 2,
      "responses": [
        {
          "answer": "Conductor cross-sectional area: 1.5 mm\u00b2; Circuit breaker nominal current: 10 A",
          "reason": "Peer 2's approach contains several errors in the application of correction factors and the final current calculation. The formula used is not standard for this type of calculation. The following is a more accurate and simplified approach:\n\n1.  **Calculate the circuit current:**\n    *   I = VA / V = 1100 VA / 220 V = 5 A\n\n2.  **Consider derating factors:**\n    *   **Ambient Temperature:** 35\u00b0C.  Since no specific derating table is provided, and assuming a common standard, the ambient temperature may not require derating. However, the conditions of installation (in a masonry wall with other circuits) suggests consideration of derating. The derating factor is dependent on the standard used and is usually obtained from tables. For the purposes of this response, we assume that the derating factor is not significantly impacting the calculation, and the current-carrying capacity of the cable is still 5A.\n    *   **Conductor grouping:** The presence of conductors from another circuit alongside the lighting circuit inside the same conduit/masonry wall will cause mutual heating and require derating. Since the number of conductors is not explicitly stated, we'll assume a common scenario and consider that the conductors are grouped.\n\n3.  **Select Conductor Size:**\n    *   Based on the calculated current of 5 A, we need to select a conductor size that can handle this current, considering the derating factors. Consulting a standard wiring table (e.g., based on IEC 60364 or a similar standard) would be necessary. For a copper conductor in a typical installation, and considering the grouping, a 1.5 mm\u00b2 conductor is often suitable for a 10A circuit. This size can typically handle currents slightly above 5A after derating. The derating factor is applied to the cable's current-carrying capacity, not the load current. The cable must still be able to carry the full load current.\n\n4.  **Select Circuit Breaker:**\n    *   The circuit breaker's nominal current should be selected to protect the cable. A common practice is to use a circuit breaker rated slightly higher than the cable's current-carrying capacity, but the rating must be no greater than the maximum current that the cable is designed to carry. A 10A circuit breaker is a standard size and is suitable for a 1.5 mm\u00b2 conductor. The circuit breaker must protect the cable from overcurrent and short-circuit situations. A 6A breaker would likely trip under normal load, and a 16A breaker would offer insufficient protection to the cable in an overload situation.\n\nTherefore, based on the above considerations:\n*   **Conductor cross-sectional area: 1.5 mm\u00b2**\n*   **Circuit breaker nominal current: 10 A**"
        },
        {
          "answer": "The conductor cross-sectional area should be 2.5 mm\u00b2 and the circuit breaker's nominal current should be 10 A.",
          "reason": "Based on the given information, the installed power of 1,100 VA and a voltage of 220 V, we can calculate the nominal current of the circuit using the formula: Power (W) = Voltage (V) * Current (A). Rearranging the formula to solve for current, we get: Current (A) = Power (W) / Voltage (V) = 1100 VA / 220 V = 5 A. However, as Peer 1 and Peer 3 both suggest the circuit breaker's nominal current should be 10 A, they likely accounted for the potential voltage drop in the conductors due to the ambient temperature and proximity to other conductors. The National Electric Code (NEC) recommends increasing the circuit ampacity by 25% for conductors installed in a masonry wall, and by 30% for conductors in a conduit. Considering this, the calculated current could be adjusted to match the suggested 10 A. The conductor's cross-sectional area should be 2.5 mm\u00b2 to carry this load. This aligns with Peer 1 and Peer 3's suggestions."
        },
        {
          "answer": "The conductor's cross-sectional area should be 2.5 mm\u00b2 and the circuit breaker's nominal current should be 5 A.",
          "reason": "Peer 2 provided a detailed calculation approach to determine the allowable current-carrying capacity of the conductor. They considered correction factors for ambient temperature, conductor material, number of conductors, and grounding, according to IEC 60287 guidelines. Using a power factor of 1 and an ambient temperature correction factor (kA) of 0.85 for 35\u00b0C, the calculation came to approximately 3.37 A. While this current is below the typical current-carrying capacity standards for a 2.5 mm\u00b2 copper conductor, it suggests a 2.5 mm\u00b2 conductor would be appropriate given common correction factors. For the circuit breaker, taking into account inrush currents and regular practice, a nominal value of around 4 A is calculated, but the standard nominal size is often chosen slightly higher for practical purposes, making 5 A more suitable."
        }
      ]
    },
    {
      "round": 3,
      "responses": [
        {
          "answer": "Peer 2 is correct.",
          "reason": "Here's the breakdown to determine the correct answer:\n\n1.  **Calculate the circuit current:**\n    *   Power (P) = 1100 VA\n    *   Voltage (V) = 220 V\n    *   Current (I) = P / V = 1100 VA / 220 V = 5 A\n\n2.  **Determine the conductor size:**\n    *   We need to consider current-carrying capacity based on installation method and ambient temperature.\n    *   The conductors are in PVC conduit embedded in a masonry wall, which is a relatively good heat dissipation scenario, but there are also other circuits nearby, which means a derating factor is needed. The ambient temperature is 35\u00b0C, which also requires a derating. We are not given the number of conductors in the conduit, so we will assume 2 (live and neutral).\n    *   We will look up the ampacity of copper conductors in PVC conduit at 35\u00b0C, and then apply any required derating factors. Without a detailed table, we'll make the following assumptions:\n        *   Assuming that the conductor is not too long, the voltage drop is not a major concern, so we are primarily concerned about the current-carrying capacity.\n        *   Given that the circuit current is 5A, the conductor must be able to carry this current safely and reliably.\n        *   2.5 mm\u00b2 copper conductors typically have an ampacity greater than 5A. The ampacity can vary depending on the insulation type, installation method, and ambient temperature. However, for a single-phase circuit with a load of 5 A, a 2.5 mm\u00b2 conductor is usually sufficient. The conductor's ampacity should be derated depending on the number of conductors in the conduit and the ambient temperature. In this case, the derating is not specified, and for this reason, 2.5mm\u00b2 copper conductors are usually acceptable.\n    *   A 2.5 mm\u00b2 conductor would be expected to handle 5 A without issue, even with some derating, but a 1.5mm\u00b2 conductor would be much closer to the limit or potentially undersized.\n\n3.  **Determine the circuit breaker size:**\n    *   The circuit breaker's nominal current should be selected to protect the conductors.\n    *   The circuit breaker should be rated to handle the circuit's normal operating current and protect the conductors from overload. The breaker should be rated at least as high as the circuit's calculated current, but not so high that the conductors are unprotected.\n    *   Typically, the circuit breaker's nominal current is chosen to be the next standard size above the calculated current, and can be a maximum of 1.25 times the continuous load current (in the case of lighting, it's considered a continuous load). So, 5 A * 1.25 = 6.25 A. The next standard size is 10 A. \n    *   A 5 A breaker would be too close to the operating current. The 10 A breaker is the more appropriate choice.\n\nTherefore, a 2.5 mm\u00b2 conductor and a 10 A circuit breaker are the most appropriate choices."
        },
        {
          "answer": "The correct answer is Peer 1: Conductor cross-sectional area: 1.5 mm\u00b2; Circuit breaker nominal current: 10 A.",
          "reason": "To determine the correct answer, we need to consider the ampacity of the conductor and the voltage drop in the circuit.\n\nFirst, we need to calculate the current drawn by the circuit. The power rating of the circuit is 1,100 VA, and the voltage is 220 V. We can use the formula:\nI = P / V\nwhere I is the current, P is the power, and V is the voltage.\n\nI = 1,100 VA / 220 V = 5 A\n\nHowever, the current calculated is the total current required by the circuit, but since it's a single-phase lighting circuit, the voltage and current are in phase and the current is not the RMS value, it is the actual value. \n\nThe actual value of the current will be slightly higher than the calculated value due to the actual voltage drop in the circuit. But we can see that the calculated value is around 5 A, which is close to the value given by Peer 3.\n\nNow, let's consider the ampacity of the conductor. The ambient temperature is 35\u00b0C, and we are using copper conductors. According to the IEC 60287 standard, the ampacity of a copper conductor can be calculated using the following formula:\nIa = (1.05 \u00d7 Ic) / (1 + (t - tc) / 75)\nwhere Ia is the ampacity, Ic is the current-carrying capacity, t is the ambient temperature, and tc is the reference temperature (30\u00b0C).\n\nHowever, this formula is a simplified version and doesn't take into account several factors, such as the conductor's cross-sectional area, the insulation type, and the circuit's configuration. \n\nFor a single-phase circuit with a 1,100 VA load, a 2.5 mm\u00b2 conductor might be sufficient for a 6 A or 8 A load, but it might be too small for a 10 A or 12 A load.\n\nBased on the given information, we can assume that the circuit breaker's nominal current is the same as the current drawn by the circuit.\n\nConsidering the above points, the correct answer is Peer 1: Conductor cross-sectional area: 1.5 mm\u00b2; Circuit breaker nominal current: 10 A."
        },
        {
          "answer": "The conductor cross-sectional area should be 2.5 mm\u00b2 and the circuit breaker's nominal current should be 10 A.",
          "reason": "The required conductor size and circuit breaker are determined by a few factors: the current demand of the circuit, the installation method, the ambient temperature, and any derating factors such as the presence of additional conductors. First, determine the current demand: 1,100 VA / 220 V = 5 A. Considering the installation conditions (running inside a conduit and derating due to ambient temperature), it's necessary to choose a conductor size that can handle more than the nominal current to ensure safety and comply with standards. A 1.5 mm\u00b2 conductor is typically rated for 15-17 A, but due to derating factors, a 2.5 mm\u00b2 conductor is often used to provide more capacity and future-proofing, ensuring the circuit's reliability and safety. The nominal current for the circuit breaker would be 10 A, aligning with standard practice to carry the circuit load while accounting for minor surges."
        }
      ]
    },
    {
      "round": 4,
      "responses": [
        {
          "answer": "The conductor cross-sectional area should be 2.5 mm\u00b2 and the circuit breaker's nominal current should be 10 A.",
          "reason": "Here's the breakdown and why Peer 3 is likely more accurate:\n\n1. **Calculate the circuit current:**\n   - Power (S) = 1100 VA\n   - Voltage (V) = 220 V\n   - Current (I) = S / V = 1100 VA / 220 V = 5 A\n\n2. **Consider the installation method and ambient temperature:**\n   - PVC conduit embedded in a masonry wall restricts heat dissipation, requiring a derating factor.\n   - The ambient temperature of 35\u00b0C is higher than the standard 30\u00b0C, also requiring a derating factor.\n   - The presence of other conductors in the conduit (from another circuit) necessitates further derating.\n\n3. **Select Conductor Size:**\n   - A 1.5 mm\u00b2 conductor is typically rated for a lower current than 5A, even before considering derating. It's unlikely to be sufficient, and the current carrying capacity is likely to be exceeded.\n   - A 2.5 mm\u00b2 conductor is generally rated for a higher current, and the derating factors will decrease the current carrying capacity, but may still be sufficient.\n\n4. **Circuit Breaker Sizing:**\n   - The circuit breaker's nominal current must be greater than or equal to the calculated current after derating, and must also protect the conductors.\n   - A 10 A circuit breaker is a common standard size and is suitable for protecting a 2.5 mm\u00b2 conductor and can handle the load.\n\n**In summary:** While a 1.5 mm\u00b2 conductor might seem sufficient based on the initial current calculation alone, the derating factors due to the installation method, ambient temperature, and bundled conductors make a larger conductor (2.5 mm\u00b2) a safer and more appropriate choice. The 10A circuit breaker provides adequate protection for this scenario."
        },
        {
          "answer": "2.5 mm\u00b2, 10 A",
          "reason": "To determine the conductor's cross-sectional area, we need to consider the installed power (1,100 VA) and the voltage (220 V). The installed power can be calculated as the product of the voltage and the current.\n\nFirst, we calculate the current in the circuit:\nI = P / V\nwhere I is the current, P is the installed power, and V is the voltage.\nI = 1,100 VA / 220 V\nI = 5 A\n\nThe next step is to choose the correct temperature correction factor for the ambient temperature of 35\u00b0C. According to the IEC 60287 standard, the temperature correction factor for 35\u00b0C is 1.11 (for copper conductors).\n\nTo determine the maximum permitted current, we need to consult the IEC 60287 standard or a similar reference for the maximum permissible temperature of copper conductors in a masonry wall. For this problem, we will assume that the maximum permissible temperature is 55\u00b0C.\n\nFor copper conductors in a masonry wall at 55\u00b0C, the maximum permitted current can be calculated as:\nI_max = 23.5 A / (sqrt((55-20)/20))\n\nAfter finding I_max, we can use the IEC 60287 standard to select a conductor that can carry the required current. \n\nWith I_max and the required current (5 A), the conductor cross-sectional area can be determined using a table or chart from the IEC 60287 standard. Based on the given information, the conductor cross-sectional area is 2.5 mm\u00b2.\n\nFor the circuit breaker's nominal current, we need to select a value that will not allow the current to exceed the maximum permitted current for the conductor. Therefore, the circuit breaker's nominal current should be 10 A, which is the value chosen by Peer 3."
        },
        {
          "answer": "Conductor cross-sectional area: 1.5 mm\u00b2; Circuit breaker nominal current: 10 A.",
          "reason": "The circuit has an installed power of 1,100 VA on a 220 V supply line, which corresponds to a nominal current of 5 A (Calculated as 1100 / 220 = 5 A). Given that the ambient temperature is 35\u00b0C and the conductors are embedded in a wall alongside another circuit, a derating factor should be applied. In most cases, for single-phase circuits with a small load like 5 A, a conductor cross-section of 1.5 mm\u00b2 is adequate under these conditions due to its current-carrying capacity, even with derating considerations. The typical circuit breaker used for such small lighting circuits is nominally 10 A in domestic wiring, which provides protection while preventing nuisance tripping under small increases in load or minor temperature variations."
        }
      ]
    },
    {
      "round": 5,
      "responses": [
        {
          "answer": "Peer 2: 2.5 mm\u00b2, 10 A",
          "reason": "Here's the breakdown of the calculation and why Peer 2 is correct:\n\n1.  **Calculate the circuit current:**\n    *   Power (S) = 1100 VA\n    *   Voltage (V) = 220 V\n    *   Current (I) = S / V = 1100 VA / 220 V = 5 A\n\n2.  **Determine the minimum conductor size based on current:**\n    *   Based on the calculated current of 5A, a 1.5 mm\u00b2 conductor would likely be sufficient in a standard scenario (check local electrical codes for specific ampacity ratings of copper conductors in PVC conduit). However, we'll continue to check for derating factors.\n\n3.  **Consider Derating Factors:**\n    *   **Ambient Temperature:** The ambient temperature is 35\u00b0C. We need to check if the conductor's ampacity needs derating due to this temperature. The temperature rating for the conductors should be known to determine the derating. (This information is missing in the problem).\n    *   **Grouping:** The problem states that other conductors are present alongside the lighting circuit. This requires derating to account for heat generated by adjacent circuits (This information is missing in the problem). The number of current-carrying conductors also affects the derating factors.\n    *   **Conduit Type:** PVC conduit is used. This impacts the thermal characteristics. (This information is missing in the problem).\n\n4. **Determine the appropriate conductor size:**\n    * Without information about the conductor's temperature rating and the number of conductors in the conduit, it's impossible to determine the precise derating factors. However, the most common conductor size chosen for general lighting circuits is 2.5 mm\u00b2 (or the next size up from the minimal size) to account for possible voltage drops, future expansion, and derating factors. With the derating factors considered, 1.5 mm\u00b2 is likely too small.\n\n5.  **Select Circuit Breaker:**\n    *   The circuit breaker's nominal current must be greater than the circuit's current but not excessively higher. A 10 A circuit breaker is the most appropriate for a 5 A circuit. It offers adequate protection without being oversized. If the current was higher, a higher amp breaker would be required.\n\n**Conclusion:**\n*   Considering the calculated current and the need to account for potential derating factors due to ambient temperature, grouping, and the need for general electrical code compliance, a 2.5 mm\u00b2 conductor and a 10 A circuit breaker are the safest and most practical choices. Peer 2 is therefore the correct answer."
        },
        {
          "answer": "Peer 1: The conductor cross-sectional area should be 2.5 mm\u00b2 and the circuit breaker's nominal current should be 10 A.",
          "reason": "The calculations involve determining the conductor's cross-sectional area based on the thermal constants of copper and the circuit's power rating. The installed power of 1,100 VA and the voltage of 220 V are used to determine the current. The current is calculated as 1,100 VA / 220 V = 5 A. \n\nSince the conductor is in a PVC conduit embedded in a masonry wall with insulated conductors nearby, it is likely operating under 'd' (touching other conductors but not in a parallel circuit) or 'e' (cable in a conduit) conditions per BS 7671, which may lead to a correction factor to be applied to the current based on the temperature (35\u00b0C). \n\nThe ambient correction factor for BS 7671 for a temperature of 35\u00b0C is typically 1.05 for 'd' conditions and 1.13 for 'e' conditions. Given the temperature and the description, we will assume 'd' conditions for this calculation. \n\nHowever, for simplicity, we'll assume a typical insulation temperature rating of 70\u00b0C for the PVC conduit and ignore the correction factor.\n\nWe'll use the formula for the ampacity of a conductor (A) as per BS 7671, which is A = I x k, where I is the design current and k is the cable ampacity factor.\n\nTo calculate the ampacity factor k, we will use the IEC 60287 formula. The formula for the ampacity factor for copper is given as k = 0.88 + (0.005 x A^(0.425)), where A is the cross-sectional area in mm\u00b2.\n\nHowever, this formula's complexity and the lack of precise information on the exact conditions of the circuit and the specific requirements of BS 7671 (e.g., the exact correction factor to apply for the ambient temperature and the exact conditions for the 'd' conditions) make it difficult to precisely calculate k and therefore A without further information.\n\nHowever, a common approach is to use a simplified version of the IEC 60287 formula: k = 0.84 + (0.003 x A^(0.37)), where A is the cross-sectional area in mm\u00b2.\n\nWe are looking for a value of A, given a design current of 5 A (ignoring the correction factor for simplicity). \n\nWe need to find the value of A that satisfies the equation:\n\n5 x k = 5.65 (The maximum conductor size for a 10 A circuit)\n\nThe k factor can be found by trial and error. \n\nPlugging in different values of A into the k equation, we find that for A = 2.5 mm\u00b2, k = 1.26, which is reasonable and in line with some tables for copper conductors.\n\nUsing the same approach, we can determine the circuit breaker's nominal current (10 A) based on standard tables for the 2.5 mm\u00b2 conductor.\n\nTherefore, Peer 1's answer appears to be correct."
        },
        {
          "answer": "The conductor cross-sectional area should be 2.5 mm\u00b2 and the circuit breaker's nominal current should be 10 A.",
          "reason": "The total power of the circuit is 1,100 VA and the voltage is 220 V. Thus, the nominal current can be calculated using the formula: I = P / V, where I is the current, P is the power, and V is the voltage. Substituting the values, we get I = 1,100 VA / 220 V = 5 A. For safety and to allow room for potential increases in load, a breaker with a nominal current of 10 A is typically chosen. Now, referring to standard reference tables, a 2.5 mm\u00b2 copper conductor can safely carry a nominal current of about 20 A under typical installation conditions, which is well above the calculated current requirement. Considering environmental factors, such as the presence of other circuits and the ambient temperature, a standard 2.5 mm\u00b2 conductor remains appropriate for the conditions described."
        }
      ]
    },
    {
      "round": 6,
      "responses": [
        {
          "answer": "The conductor cross-sectional area should be 2.5 mm\u00b2 and the circuit breaker's nominal current should be 10 A.",
          "reason": "Here's how to determine the answer:\n\n1.  **Calculate the current (I):**\n    *   I = P / V  where P is power (VA) and V is voltage (V).\n    *   I = 1100 VA / 220 V = 5 A\n\n2.  **Determine the conductor size (based on current and derating):**\n    *   We need to consider the ambient temperature (35\u00b0C) and the presence of other circuits. This will affect the ampacity of the conductor. Because of the limited information provided, and without access to specific tables for derating factors based on all parameters (e.g., the exact number of other circuits, their loading, etc.), we will assume the standard ampacity of a 2.5 mm\u00b2 copper conductor is sufficient. A 2.5 mm\u00b2 conductor is generally rated for more than 5A under the conditions specified. However, without full knowledge of all derating factors, it's difficult to be 100% certain.\n\n3.  **Determine the circuit breaker size:**\n    *   The circuit breaker should be sized to protect the conductors. It needs to be larger than the calculated current, but not significantly larger. A 10 A circuit breaker is the standard size above 5A and would adequately protect a 2.5 mm\u00b2 conductor in this scenario, while allowing the circuit to operate normally.\n\nTherefore, based on the given information and standard electrical practices, a 2.5 mm\u00b2 conductor and a 10 A circuit breaker are the appropriate choices. The peer responses are correct."
        },
        {
          "answer": "2.5 mm\u00b2 and 10 A",
          "reason": "A single-phase lighting circuit with 1,100 VA power can be determined as follows:\n\nFirst, we need to calculate the current in the circuit. We know that power (P) in VA is equal to the product of voltage (V) and current (I): P = V * I.\nRearranging the formula to solve for current: I = P / V\nGiven P = 1,100 VA and V = 220 V, we can calculate the current: I = 1,100 / 220 = 5 A\n\nHowever, this is a basic calculation and does not take into account the ambient temperature and other factors affecting the conductor.\n\nThe IEC 60364 standard recommends a correction factor for the ambient temperature. \nThe correction factor for a temperature difference of 35\u00b0C above the reference temperature (20\u00b0C) is:\n\u0394t = 35\u00b0C\nCorrection factor (Kc) = 1 + (\u0394t / 20)\nKc = 1 + (35 / 20) = 2.75\n\nAccording to the standard, the maximum conductor temperature should not exceed 70\u00b0C.\nThe maximum permitted temperature rise (\u0394t) is 70 - 20 = 50\u00b0C\n\nHowever, we don't need to apply this because the ambient temperature is the limiting factor.\n\nNow let's use the IEC 60287 standard for the conductor sizing. We need to determine the maximum permitted current for the given conductor and ambient temperature.\n\nThe formula to determine the maximum permitted current (I) is:\nI = \u221a(k * A * (T / \u0394t))\nwhere:\n- k is the temperature correction factor (k = 115 for copper at 70\u00b0C)\n- A is the cross-sectional area of the conductor in mm\u00b2\n- T is the maximum permitted conductor temperature in \u00b0C (T = 70)\n- \u0394t is the temperature difference between the conductor and the ambient (\u0394t = 35\u00b0C)\n\nWe know that the peer 1 and peer 3's answer is 2.5 mm\u00b2. Let's verify it:\n\nI = \u221a(115 * 2.5 * (70 / 35))\nI = \u221a(115 * 2.5 * 2)\nI = \u221a(575)\nI \u2248 24 A\n\nHowever, this is not the current required for our circuit. Our circuit's current is 5 A.\n\nThe peer 1 and peer 3's answer does not take into account this correction factor. \nHowever, for the given conditions, their answer might seem correct due to the simplification above.\n\nThe correct approach is to use the IEC 60287 standard to determine the maximum permitted current for the given conductor and ambient temperature.\n\nFor a more accurate answer, let's refer to the IEC 60364 standard. The standard recommends that for a single-phase circuit, the nominal current of the circuit breaker should be determined by the following formula:\nIcn = (P / V) / Kc\nwhere:\n- Icn is the nominal current of the circuit breaker\n- P is the power in VA\n- V is the voltage\n- Kc is the correction factor\n\nIcn = (1,100 / 220) / 1\nIcn = 5 A\n\nThe maximum permitted current for the given conductor and ambient temperature is the limiting factor.\n\nHowever, there is no clear data on the maximum permitted current for the given conductor and ambient temperature in the peer's answer.\n\nThe answer given by peer 1 and peer 3 (2.5 mm\u00b2 and 10 A) might not be correct based on these calculations.\n\nHowever, for a more accurate answer, let's follow the IEC 60287 standard.\n\nAccording to the IEC 60287 standard, for a copper conductor with a cross-sectional area of 2.5 mm\u00b2 and an ambient temperature of 35\u00b0C, the maximum permitted current is approximately 11 A.\n\nHowever, for the given circuit with a power of 1,100 VA, the required current is 5 A.\n\nThe correct approach is to use the IEC 60364 standard to determine the nominal current of the circuit breaker.\n\nAccording to the IEC 60364 standard, the nominal current of the circuit breaker should be determined by the following formula:\nIcn = (P / V) / Kc\nwhere:\n- Icn is the nominal current of the circuit breaker\n- P is the power in VA\n- V is the voltage\n- Kc is the correction factor\n\nIcn = (1,100 / 220) / 1\nIcn = 5 A\n\nHowever, this is not the answer given by peer 1 and peer 3.\n\nThe IEC 60364 standard also recommends that for a single-phase circuit, the nominal current of the circuit breaker should be determined by the following formula:\nIcn = (P / V) / Kc * Kf\nwhere:\n- Icn is the nominal current of the circuit breaker\n- P is the power in VA\n- V is the voltage\n- Kc is the correction factor\n- Kf is the coefficient for the number of conductors in the conduit\n\nThe coefficient Kf depends on the number of conductors in the conduit.\n\nFor the given conditions, let's assume that the number of conductors is 5.\n\nThe value of Kf can be determined from the IEC 60364 standard.\n\nHowever, the standard does not provide a clear value for Kf.\n\nFor a more accurate answer, the value of Kf should be determined experimentally or by referring to a specific standard.\n\nConsidering the limitations above, the answer given by peer 1 and peer 3 might be acceptable for the given conditions.\n\nHowever, for a more accurate answer, the IEC 60287 standard should be used to determine the maximum permitted current for the given conductor and ambient temperature.\n\nBased on the given information, it seems that the answer given by peer 1 and peer 3 is 2.5 mm\u00b2 and 10 A."
        },
        {
          "answer": "2.5 mm\u00b2, 10 A",
          "reason": "Given the installed power of 1,100 VA and a voltage of 220 V, the circuit's current can be calculated as I = P/V = 1,100 VA / 220 V = 5 A. Considering the presence of other circuits and a higher ambient temperature, a correction factor m